TY  - CONF
AU  - Buzurović, Ivan M.
AU  - Debeljković, Dragutin Lj.
AU  - Sedak, Miloš
AU  - Radojević, Darko
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2986
AB  - This paper provides novel additional sufficient conditions for finite-time stability of the linear continuous singular time delay systems. A novel method was used to derive new delay dependent conditions. The stability of the system was analyzed using both the Lyapunov-like approach and the Jensen's and Coppel's inequality, including the convolution of delayed states. The derived conditions were applied in the system stability analysis. As a result of these, the aggregation functional did not have to be positive in the state space domain and did not need to have the negative derivatives along the system trajectories. Finite-time stability was analyzed using the novel conditions derived in this paper, which guarantees that the states of the systems do not exceed the predefined boundaries over a finite-time interval.
PB  - Institute of Electrical and Electronics Engineers Inc.
C3  - Proceedings of the 2017 12th IEEE Conference on Industrial Electronics and Applications, ICIEA 2017
T1  - Further Results on Finite-time Stability of Continuous Singular Time Delay Systems
EP  - 1545
SP  - 1540
VL  - 2018-February
DO  - 10.1109/ICIEA.2017.8283083
ER  - 

@conference{
author = "Buzurović, Ivan M. and Debeljković, Dragutin Lj. and Sedak, Miloš and Radojević, Darko",
year = "2018",
abstract = "This paper provides novel additional sufficient conditions for finite-time stability of the linear continuous singular time delay systems. A novel method was used to derive new delay dependent conditions. The stability of the system was analyzed using both the Lyapunov-like approach and the Jensen's and Coppel's inequality, including the convolution of delayed states. The derived conditions were applied in the system stability analysis. As a result of these, the aggregation functional did not have to be positive in the state space domain and did not need to have the negative derivatives along the system trajectories. Finite-time stability was analyzed using the novel conditions derived in this paper, which guarantees that the states of the systems do not exceed the predefined boundaries over a finite-time interval.",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
journal = "Proceedings of the 2017 12th IEEE Conference on Industrial Electronics and Applications, ICIEA 2017",
title = "Further Results on Finite-time Stability of Continuous Singular Time Delay Systems",
pages = "1545-1540",
volume = "2018-February",
doi = "10.1109/ICIEA.2017.8283083"
}

Buzurović, I. M., Debeljković, D. Lj., Sedak, M.,& Radojević, D.. (2018). Further Results on Finite-time Stability of Continuous Singular Time Delay Systems. in Proceedings of the 2017 12th IEEE Conference on Industrial Electronics and Applications, ICIEA 2017
Institute of Electrical and Electronics Engineers Inc.., 2018-February, 1540-1545.
https://doi.org/10.1109/ICIEA.2017.8283083

Buzurović IM, Debeljković DL, Sedak M, Radojević D. Further Results on Finite-time Stability of Continuous Singular Time Delay Systems. in Proceedings of the 2017 12th IEEE Conference on Industrial Electronics and Applications, ICIEA 2017. 2018;2018-February:1540-1545.
doi:10.1109/ICIEA.2017.8283083 .

Buzurović, Ivan M., Debeljković, Dragutin Lj., Sedak, Miloš, Radojević, Darko, "Further Results on Finite-time Stability of Continuous Singular Time Delay Systems" in Proceedings of the 2017 12th IEEE Conference on Industrial Electronics and Applications, ICIEA 2017, 2018-February (2018):1540-1545,
https://doi.org/10.1109/ICIEA.2017.8283083 . .

TY  - BOOK
AU  - Matijević, Milan
AU  - Debeljković, Dragutin
AU  - Buzurović, Ivan
AU  - Lazarević, Mihailo
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6754
AB  - Okosnica ove monografije počiva na savremenoj teoriji upravljanja i postavlja i razrešava niz veoma složenih pitanja dinamike, posebnih klasa, sistema automatskog upravljanja,  opisanih sistemom diferencijalnih (diferencnih)  jednačina sa pomerenim argumentom. U tom smislu, izložen je ograničen broj radova eminentnih naučnika i osvedočenih autoriteta iz ove oblasti, kao i manji broj radova samih autora iz ove, uvek aktuelne i više nego provokativne, oblasti savremene teorije upravljanja i stabilnosti. Poseban doprinos monografije daje pregled upravljačkih struktura sa unutrašnjim modelima. Opisana su tri globalna prilaza sinteze sistema sa unutrašnjim modelima koja se odnose na korišćenje: principa unutrašnjeg modela IMP (Internal Model Principle), IMC (Internal Model Control) strukture i Tsypkinove IMPACT (Internal Model Principle and Control Together) strukture. Ovi prilazi su nastali potpuno nezavisno jedni od drugih, u različitim vremenskim razdobljima, kao plod rada mnoštva istraživača, angažovanih na rešavanju različitih upravljačkih problema. U ovim upravljačkim strukturama ugrađuju se elementi čiji karakter eksplicitno zavisi od modela poremećaja i/ili modela objekta upravljanja. Zavisno od primarnih upravljačkih ciljeva, razvijeni su različiti koncepti primene unutrašnjih modela u strukturnoj sintezi sistema. U monografiji su opisana svojstva struktura sa unutrašnjim modelima. Svi do sada razvijeni postupci strukturne sinteze upravljanih sporih industrijskih procesa mogu se svrstati u pomenute tri kategorije u zavisnosti od toga kako se i na kom principu unutrašnji modeli unose u upravljački deo strukture sistema automatskog upravljanja. Posebno poglavlje je posvećeno novoj upravljačkoj strukturi za upravljanje sporih industrijskih procesa sa transportnim kašenjenjem. Odlikuje je mali broj podešljivih parametara sa jasnim fizičkim značenjem i eksplicitnim uticajem na dinamičke i robustne performanse sistema sa zatvorenom povratnom spregom. Sistematizacija i strukturne i parametarske sinteze IMPACT strukture, i njenih osnovnih varijacija, je data u poslednjem poglavlju.
PB  - Univerzitet u Kragujevcu Fakultet inženjerskih nauka
T2  - Univerzitet u Kragujevcu  Fakultet inženjerskih nauka Kragujevac     (COBISS.SR – ID 224376588)
T1  - Dinamika sistema opisanih algebro-diferencijalnim jednačinama sa pomerenim argumentom, II deo
EP  - 570
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6754
ER  - 

@book{
author = "Matijević, Milan and Debeljković, Dragutin and Buzurović, Ivan and Lazarević, Mihailo",
year = "2017",
abstract = "Okosnica ove monografije počiva na savremenoj teoriji upravljanja i postavlja i razrešava niz veoma složenih pitanja dinamike, posebnih klasa, sistema automatskog upravljanja,  opisanih sistemom diferencijalnih (diferencnih)  jednačina sa pomerenim argumentom. U tom smislu, izložen je ograničen broj radova eminentnih naučnika i osvedočenih autoriteta iz ove oblasti, kao i manji broj radova samih autora iz ove, uvek aktuelne i više nego provokativne, oblasti savremene teorije upravljanja i stabilnosti. Poseban doprinos monografije daje pregled upravljačkih struktura sa unutrašnjim modelima. Opisana su tri globalna prilaza sinteze sistema sa unutrašnjim modelima koja se odnose na korišćenje: principa unutrašnjeg modela IMP (Internal Model Principle), IMC (Internal Model Control) strukture i Tsypkinove IMPACT (Internal Model Principle and Control Together) strukture. Ovi prilazi su nastali potpuno nezavisno jedni od drugih, u različitim vremenskim razdobljima, kao plod rada mnoštva istraživača, angažovanih na rešavanju različitih upravljačkih problema. U ovim upravljačkim strukturama ugrađuju se elementi čiji karakter eksplicitno zavisi od modela poremećaja i/ili modela objekta upravljanja. Zavisno od primarnih upravljačkih ciljeva, razvijeni su različiti koncepti primene unutrašnjih modela u strukturnoj sintezi sistema. U monografiji su opisana svojstva struktura sa unutrašnjim modelima. Svi do sada razvijeni postupci strukturne sinteze upravljanih sporih industrijskih procesa mogu se svrstati u pomenute tri kategorije u zavisnosti od toga kako se i na kom principu unutrašnji modeli unose u upravljački deo strukture sistema automatskog upravljanja. Posebno poglavlje je posvećeno novoj upravljačkoj strukturi za upravljanje sporih industrijskih procesa sa transportnim kašenjenjem. Odlikuje je mali broj podešljivih parametara sa jasnim fizičkim značenjem i eksplicitnim uticajem na dinamičke i robustne performanse sistema sa zatvorenom povratnom spregom. Sistematizacija i strukturne i parametarske sinteze IMPACT strukture, i njenih osnovnih varijacija, je data u poslednjem poglavlju.",
publisher = "Univerzitet u Kragujevcu Fakultet inženjerskih nauka",
journal = "Univerzitet u Kragujevcu  Fakultet inženjerskih nauka Kragujevac     (COBISS.SR – ID 224376588)",
title = "Dinamika sistema opisanih algebro-diferencijalnim jednačinama sa pomerenim argumentom, II deo",
pages = "570-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6754"
}

Matijević, M., Debeljković, D., Buzurović, I.,& Lazarević, M.. (2017). Dinamika sistema opisanih algebro-diferencijalnim jednačinama sa pomerenim argumentom, II deo. in Univerzitet u Kragujevcu  Fakultet inženjerskih nauka Kragujevac     (COBISS.SR – ID 224376588)
Univerzitet u Kragujevcu Fakultet inženjerskih nauka., 1-570.
https://hdl.handle.net/21.15107/rcub_machinery_6754

Matijević M, Debeljković D, Buzurović I, Lazarević M. Dinamika sistema opisanih algebro-diferencijalnim jednačinama sa pomerenim argumentom, II deo. in Univerzitet u Kragujevcu  Fakultet inženjerskih nauka Kragujevac     (COBISS.SR – ID 224376588). 2017;:1-570.
https://hdl.handle.net/21.15107/rcub_machinery_6754 .

Matijević, Milan, Debeljković, Dragutin, Buzurović, Ivan, Lazarević, Mihailo, "Dinamika sistema opisanih algebro-diferencijalnim jednačinama sa pomerenim argumentom, II deo" in Univerzitet u Kragujevcu  Fakultet inženjerskih nauka Kragujevac     (COBISS.SR – ID 224376588) (2017):1-570,
https://hdl.handle.net/21.15107/rcub_machinery_6754 .

TY  - CONF
AU  - Buzurović, Ivan M.
AU  - Debeljković, Dragutin Lj.
AU  - Sedak, Miloš
AU  - Radojević, Darko
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2700
AB  - This paper provides sufficient conditions for the finite time stability of linear time invariant discrete descriptor time delay systems, mathematically described as Ex(k+1) = A(0)x(k) + A(1)x(t-h). A novel method was used to derive new delay dependent conditions. Stability of the system was analyzed using both the Lyapunov-like approach and the Jensen's inequality, including convolution of delayed states. The established conditions were applied to analysis of the system stability. In this case, the aggregation functional does not have to be positive in the state space domain and does not need to have the negative derivatives along the system trajectories. The system stability conditions were applicable to investigation of the finite time stability using the novel conditions proposed in this paper. This mathematical formulation guaranteed that the states of the systems do not exceed the predefined boundaries over a finite time interval.
PB  - Institute of Electrical and Electronics Engineers Inc.
C3  - 2016 14th International Conference on Control, Automation, Robotics and Vision, ICARCV 2016
T1  - Finite-Time Stability Analysis of Descriptor Discrete Time-Delay Systems Using Discrete Convolution of Delayed States
DO  - 10.1109/ICARCV.2016.7838794
ER  - 

@conference{
author = "Buzurović, Ivan M. and Debeljković, Dragutin Lj. and Sedak, Miloš and Radojević, Darko",
year = "2017",
abstract = "This paper provides sufficient conditions for the finite time stability of linear time invariant discrete descriptor time delay systems, mathematically described as Ex(k+1) = A(0)x(k) + A(1)x(t-h). A novel method was used to derive new delay dependent conditions. Stability of the system was analyzed using both the Lyapunov-like approach and the Jensen's inequality, including convolution of delayed states. The established conditions were applied to analysis of the system stability. In this case, the aggregation functional does not have to be positive in the state space domain and does not need to have the negative derivatives along the system trajectories. The system stability conditions were applicable to investigation of the finite time stability using the novel conditions proposed in this paper. This mathematical formulation guaranteed that the states of the systems do not exceed the predefined boundaries over a finite time interval.",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
journal = "2016 14th International Conference on Control, Automation, Robotics and Vision, ICARCV 2016",
title = "Finite-Time Stability Analysis of Descriptor Discrete Time-Delay Systems Using Discrete Convolution of Delayed States",
doi = "10.1109/ICARCV.2016.7838794"
}

Buzurović, I. M., Debeljković, D. Lj., Sedak, M.,& Radojević, D.. (2017). Finite-Time Stability Analysis of Descriptor Discrete Time-Delay Systems Using Discrete Convolution of Delayed States. in 2016 14th International Conference on Control, Automation, Robotics and Vision, ICARCV 2016
Institute of Electrical and Electronics Engineers Inc...
https://doi.org/10.1109/ICARCV.2016.7838794

Buzurović IM, Debeljković DL, Sedak M, Radojević D. Finite-Time Stability Analysis of Descriptor Discrete Time-Delay Systems Using Discrete Convolution of Delayed States. in 2016 14th International Conference on Control, Automation, Robotics and Vision, ICARCV 2016. 2017;.
doi:10.1109/ICARCV.2016.7838794 .

Buzurović, Ivan M., Debeljković, Dragutin Lj., Sedak, Miloš, Radojević, Darko, "Finite-Time Stability Analysis of Descriptor Discrete Time-Delay Systems Using Discrete Convolution of Delayed States" in 2016 14th International Conference on Control, Automation, Robotics and Vision, ICARCV 2016 (2017),
https://doi.org/10.1109/ICARCV.2016.7838794 . .

TY  - JOUR
AU  - Debeljković, Dragutin Lj.
AU  - Cvetković, Aleksandar
AU  - Buzurović, Ivan
AU  - Mišić, Milan
AU  - Janković, Vladimir
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2057
AB  - U ovom radu razmatra se jedno moguće rešenje bazične nelinearne kvadratne matrične jednačine. To rešenje ima krucijelni značaj u formulisanju posebnog kriterijuma, zavisnog od iznosa čisto vremenskog kašnjenja, za stabilnost na konačnom vremenskom intervalu posebne klase sistema sa kašnjenjem, opisane svojim matričnim modelom x(k+1)=A0(k) + A1x(k-h). U tom smislu izveden je i odgovarajući kriterijum stabilnosti koji uključuje i iznos čisto vremenskog kašnjenja. Mimo toga, posebno je apostrofiran značaj nelinearnog diskretnog matričnog polinoma u stabilnosti sistema. Koristeći matematički formalizam, baziran na Traub-ovom i Bernuli-jevom algoritmu, zaključeno je da sračunavanje dominantnog solventa matričnog polinoma, ne garantuje potrebnu konvergenciju u svim slučajevima, kao sto je slučaj u tradicionalnim numeričkim procedurama. U ovom radu, prezentuje se jedno posebno i jedno opste rešenje, koje važi za slučaj kada se matrični polinom može prikazati u faktorizovanom obliku. Numeričkim primerom ilustrovana je opravdanost predložene procedure.
AB  - In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1)=A0(k)+A1x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular and one general solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results.
PB  - Vojnotehnički institut, Beograd
T2  - Scientific Technical Review
T1  - Stabilnost na konačnom vremenskom intervalu, zavisna od kašnjenja, linearnih diskretnih sistema sa kašnjenjem - prilaz sa pozicija numeričkog rešavanja
T1  - Stabilité sur l'intervalle temporelle finie dépendante du délai des systèmes linéaires discrets à délai: Tableau de solution numérique / (ruski) Stabil'nost' v sistemah konečnogo vremeni v zavisimosti ot zaderžek, linejnyh diskretnyh sistem so zaderžkoj vremeni: Displej s pokazom čislennyh rešenij
T1  - On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach
EP  - 45
IS  - 3
SP  - 39
VL  - 65
DO  - 10.5937/STR1503039D
ER  - 

@article{
author = "Debeljković, Dragutin Lj. and Cvetković, Aleksandar and Buzurović, Ivan and Mišić, Milan and Janković, Vladimir",
year = "2015",
abstract = "U ovom radu razmatra se jedno moguće rešenje bazične nelinearne kvadratne matrične jednačine. To rešenje ima krucijelni značaj u formulisanju posebnog kriterijuma, zavisnog od iznosa čisto vremenskog kašnjenja, za stabilnost na konačnom vremenskom intervalu posebne klase sistema sa kašnjenjem, opisane svojim matričnim modelom x(k+1)=A0(k) + A1x(k-h). U tom smislu izveden je i odgovarajući kriterijum stabilnosti koji uključuje i iznos čisto vremenskog kašnjenja. Mimo toga, posebno je apostrofiran značaj nelinearnog diskretnog matričnog polinoma u stabilnosti sistema. Koristeći matematički formalizam, baziran na Traub-ovom i Bernuli-jevom algoritmu, zaključeno je da sračunavanje dominantnog solventa matričnog polinoma, ne garantuje potrebnu konvergenciju u svim slučajevima, kao sto je slučaj u tradicionalnim numeričkim procedurama. U ovom radu, prezentuje se jedno posebno i jedno opste rešenje, koje važi za slučaj kada se matrični polinom može prikazati u faktorizovanom obliku. Numeričkim primerom ilustrovana je opravdanost predložene procedure., In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1)=A0(k)+A1x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular and one general solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results.",
publisher = "Vojnotehnički institut, Beograd",
journal = "Scientific Technical Review",
title = "Stabilnost na konačnom vremenskom intervalu, zavisna od kašnjenja, linearnih diskretnih sistema sa kašnjenjem - prilaz sa pozicija numeričkog rešavanja, Stabilité sur l'intervalle temporelle finie dépendante du délai des systèmes linéaires discrets à délai: Tableau de solution numérique / (ruski) Stabil'nost' v sistemah konečnogo vremeni v zavisimosti ot zaderžek, linejnyh diskretnyh sistem so zaderžkoj vremeni: Displej s pokazom čislennyh rešenij, On finite time delay dependent stability of linear discrete delay systems: Numerical solution approach",
pages = "45-39",
number = "3",
volume = "65",
doi = "10.5937/STR1503039D"
}

Debeljković, D. Lj., Cvetković, A., Buzurović, I., Mišić, M.,& Janković, V.. (2015). Stabilnost na konačnom vremenskom intervalu, zavisna od kašnjenja, linearnih diskretnih sistema sa kašnjenjem - prilaz sa pozicija numeričkog rešavanja. in Scientific Technical Review
Vojnotehnički institut, Beograd., 65(3), 39-45.
https://doi.org/10.5937/STR1503039D

Debeljković DL, Cvetković A, Buzurović I, Mišić M, Janković V. Stabilnost na konačnom vremenskom intervalu, zavisna od kašnjenja, linearnih diskretnih sistema sa kašnjenjem - prilaz sa pozicija numeričkog rešavanja. in Scientific Technical Review. 2015;65(3):39-45.
doi:10.5937/STR1503039D .

Debeljković, Dragutin Lj., Cvetković, Aleksandar, Buzurović, Ivan, Mišić, Milan, Janković, Vladimir, "Stabilnost na konačnom vremenskom intervalu, zavisna od kašnjenja, linearnih diskretnih sistema sa kašnjenjem - prilaz sa pozicija numeričkog rešavanja" in Scientific Technical Review, 65, no. 3 (2015):39-45,
https://doi.org/10.5937/STR1503039D . .

TY  - CONF
AU  - Buzurović, Ivan
AU  - Cvetković, Aleksandar
AU  - Debeljković, Dragutin Lj.
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2209
AB  - In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1) = A0(k) + A1x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results.
PB  - Destech Publications, Inc, Lancaster
C3  - 2015 International Conference on Applied Mechanics and Mechatronics Engineering (Amme 2015)
T1  - Delay Dependent Finite Time Stability of Discrete Time Delay Systems: Towards the New Solution
EP  - 233
SP  - 228
UR  - https://hdl.handle.net/21.15107/rcub_machinery_2209
ER  - 

@conference{
author = "Buzurović, Ivan and Cvetković, Aleksandar and Debeljković, Dragutin Lj.",
year = "2015",
abstract = "In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1) = A0(k) + A1x(k-h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete polynomial matrix equation is explained. With the use of the mathematical formalism based on the Traub and Bernoulli's algorithms, it was concluded that the computation of the dominant solvent of the matrix polynomial equation does not guarantee a necessary convergence in all cases, unlike in the traditional numerical procedures. In this paper, we presented one particular solution valid in the case when the discrete matrix equation was presented in its factorial form. The numerical computations are performed to illustrate the suggested results.",
publisher = "Destech Publications, Inc, Lancaster",
journal = "2015 International Conference on Applied Mechanics and Mechatronics Engineering (Amme 2015)",
title = "Delay Dependent Finite Time Stability of Discrete Time Delay Systems: Towards the New Solution",
pages = "233-228",
url = "https://hdl.handle.net/21.15107/rcub_machinery_2209"
}

Buzurović, I., Cvetković, A.,& Debeljković, D. Lj.. (2015). Delay Dependent Finite Time Stability of Discrete Time Delay Systems: Towards the New Solution. in 2015 International Conference on Applied Mechanics and Mechatronics Engineering (Amme 2015)
Destech Publications, Inc, Lancaster., 228-233.
https://hdl.handle.net/21.15107/rcub_machinery_2209

Buzurović I, Cvetković A, Debeljković DL. Delay Dependent Finite Time Stability of Discrete Time Delay Systems: Towards the New Solution. in 2015 International Conference on Applied Mechanics and Mechatronics Engineering (Amme 2015). 2015;:228-233.
https://hdl.handle.net/21.15107/rcub_machinery_2209 .

Buzurović, Ivan, Cvetković, Aleksandar, Debeljković, Dragutin Lj., "Delay Dependent Finite Time Stability of Discrete Time Delay Systems: Towards the New Solution" in 2015 International Conference on Applied Mechanics and Mechatronics Engineering (Amme 2015) (2015):228-233,
https://hdl.handle.net/21.15107/rcub_machinery_2209 .

TY  - JOUR
AU  - Debeljković, Dragutin Lj.
AU  - Buzurović, Ivan
AU  - Matija, Lidija
AU  - Koruga, Đuro
PY  - 2013
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1611
AB  - U ovom radu izvedeni su dovoljni uslovi praktične stabilnosti i stabilnosti na konačnom vremenskom intervalu za klasu linearnih vremenski neprekidnih singularnih sistema sa čistim vremenskim kašnjenjem. Singularni sistemi i singularni sistemi sa čistim vremenskim kašnjenjem mogu biti matematički opisani jednačinama tipa: Ex(t) = Ax(t) i Ex(t) = A0x(t) - A1x(t - ), sledstveno. Analizirajući stabilnost na konačnom vremenskom intervalu izvedeni su novi uslovi, i to zavisni i nezavisni od vremenskog kašnjenja. Predloženi prilaz se zasniva na upotrebi Ljapunovljevih funkcija i njihovim osobinama na potprostoru konzistentinh početnih funkcija ili uslova. Ove funkcije ne moraju biti pozitivno određene u celom prostoru stanja, niti negativno određene duž trajektorija sistema. Kada se razmatra praktična stabilnost, ovaj prilaz se kombinuje sa klasičnom ljapunovskom tehnikom koja garantuje osobinu privlačenja sistema. U cilju dobijanja manje konzervativnih rezultata, korišćena je i LMI metoda. Predloženi metod primenjen je i testiran na jednom medicinskom robotskom sistemu. Sistem je dizajniran za različite namene, kao što su automatska isporuka medikamenata, biopsija ili isporuka radioaktivnih zrnaca unutar obolelog tkiva. Za takav sistem razvijena je posebna tehnika modeliranja, upravljanja i analize stabilnosti opisanog sistema. U svrhu matematičkog modeliranja, sistem je dekomponovan na mehanički deo i na radnu okolinu koja presudno utiče na dinamičko ponašanje. Ovakav pristup se pokazao adekvatnim u slučaju kada spoljašnje sile utiču na dinamiku sistema. Dobijen matematički model se analizira kao singularni sistem automatskog upravljanja. U slučaju kada se uticaj spoljašnjih sila može zanemariti, dinamičko ponašanje se analizira klasičnim metodama teorije upravljanja.
AB  - In this paper sufficient conditions for both practical and finite time stability of linear singular continuous time delay systems were introduced. The singular and singular time delay systems can be mathematically described as Ex (t) = Ax (t) and Ex (t) = A0x (t) + A1x (t-), respectively. Analyzing finite time stability, the new delay independent and delay dependent conditions were derived using the approaches based on Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to be positive on the whole state space and to have negative derivatives along the system trajectories. When the practical stability was analyzed, the approach was combined with classical Lyapunov technique to guarantee the attractivity property of the system behavior. Furthermore, an LMI approach was applied to obtain less conservative stability conditions. The proposed methodology was applied and tested on a medical robotic system. The system was designed for different insertion tasks playing important roles in automatic drug delivery, biopsy or radioactive seeds delivery. In this paper we have summarized different techniques for adequate modeling, control and stability analysis of the medical robots. The model of the robotic system, with the tasks described above, the entire system can be decomposed to the robotic subsystem and the environment subsystem. Modeling of the system by the method mentioned has been proved to be suitable when the force appears as a result of the interaction of the two subsystems. The mathematical model of the system has a singular characteristic. The singular system theory could be applied to the case described. It is well known that all mechanical systems have some delay. In that case a theory of singular systems with delayed states may be applied, as well. For the second phase in which there is no interaction, the dynamic behavior can be analyzed by the classic theory.
T2  - Contemporary materials
T1  - Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova
T1  - Non-Lyapunov stability of singular systems: Classical and modern approaches with application to automatic drug delivery
EP  - 32
IS  - 1
SP  - 22
VL  - 4
DO  - 10.7251/COMEN1301022D
ER  - 

@article{
author = "Debeljković, Dragutin Lj. and Buzurović, Ivan and Matija, Lidija and Koruga, Đuro",
year = "2013",
abstract = "U ovom radu izvedeni su dovoljni uslovi praktične stabilnosti i stabilnosti na konačnom vremenskom intervalu za klasu linearnih vremenski neprekidnih singularnih sistema sa čistim vremenskim kašnjenjem. Singularni sistemi i singularni sistemi sa čistim vremenskim kašnjenjem mogu biti matematički opisani jednačinama tipa: Ex(t) = Ax(t) i Ex(t) = A0x(t) - A1x(t - ), sledstveno. Analizirajući stabilnost na konačnom vremenskom intervalu izvedeni su novi uslovi, i to zavisni i nezavisni od vremenskog kašnjenja. Predloženi prilaz se zasniva na upotrebi Ljapunovljevih funkcija i njihovim osobinama na potprostoru konzistentinh početnih funkcija ili uslova. Ove funkcije ne moraju biti pozitivno određene u celom prostoru stanja, niti negativno određene duž trajektorija sistema. Kada se razmatra praktična stabilnost, ovaj prilaz se kombinuje sa klasičnom ljapunovskom tehnikom koja garantuje osobinu privlačenja sistema. U cilju dobijanja manje konzervativnih rezultata, korišćena je i LMI metoda. Predloženi metod primenjen je i testiran na jednom medicinskom robotskom sistemu. Sistem je dizajniran za različite namene, kao što su automatska isporuka medikamenata, biopsija ili isporuka radioaktivnih zrnaca unutar obolelog tkiva. Za takav sistem razvijena je posebna tehnika modeliranja, upravljanja i analize stabilnosti opisanog sistema. U svrhu matematičkog modeliranja, sistem je dekomponovan na mehanički deo i na radnu okolinu koja presudno utiče na dinamičko ponašanje. Ovakav pristup se pokazao adekvatnim u slučaju kada spoljašnje sile utiču na dinamiku sistema. Dobijen matematički model se analizira kao singularni sistem automatskog upravljanja. U slučaju kada se uticaj spoljašnjih sila može zanemariti, dinamičko ponašanje se analizira klasičnim metodama teorije upravljanja., In this paper sufficient conditions for both practical and finite time stability of linear singular continuous time delay systems were introduced. The singular and singular time delay systems can be mathematically described as Ex (t) = Ax (t) and Ex (t) = A0x (t) + A1x (t-), respectively. Analyzing finite time stability, the new delay independent and delay dependent conditions were derived using the approaches based on Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to be positive on the whole state space and to have negative derivatives along the system trajectories. When the practical stability was analyzed, the approach was combined with classical Lyapunov technique to guarantee the attractivity property of the system behavior. Furthermore, an LMI approach was applied to obtain less conservative stability conditions. The proposed methodology was applied and tested on a medical robotic system. The system was designed for different insertion tasks playing important roles in automatic drug delivery, biopsy or radioactive seeds delivery. In this paper we have summarized different techniques for adequate modeling, control and stability analysis of the medical robots. The model of the robotic system, with the tasks described above, the entire system can be decomposed to the robotic subsystem and the environment subsystem. Modeling of the system by the method mentioned has been proved to be suitable when the force appears as a result of the interaction of the two subsystems. The mathematical model of the system has a singular characteristic. The singular system theory could be applied to the case described. It is well known that all mechanical systems have some delay. In that case a theory of singular systems with delayed states may be applied, as well. For the second phase in which there is no interaction, the dynamic behavior can be analyzed by the classic theory.",
journal = "Contemporary materials",
title = "Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova, Non-Lyapunov stability of singular systems: Classical and modern approaches with application to automatic drug delivery",
pages = "32-22",
number = "1",
volume = "4",
doi = "10.7251/COMEN1301022D"
}

Debeljković, D. Lj., Buzurović, I., Matija, L.,& Koruga, Đ.. (2013). Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova. in Contemporary materials, 4(1), 22-32.
https://doi.org/10.7251/COMEN1301022D

Debeljković DL, Buzurović I, Matija L, Koruga Đ. Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova. in Contemporary materials. 2013;4(1):22-32.
doi:10.7251/COMEN1301022D .

Debeljković, Dragutin Lj., Buzurović, Ivan, Matija, Lidija, Koruga, Đuro, "Neljapunovska stabilnost singularnih sistema - klasičan i moderan prilaz sa primenom u automatskoj isporuci lekova" in Contemporary materials, 4, no. 1 (2013):22-32,
https://doi.org/10.7251/COMEN1301022D . .