Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems
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2014
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Prikaz svih podataka o dokumentuApstrakt
In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It
was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular class of linear discrete time-delay systems are derived. These results are modified and used for checking the stability of discrete-time fractional order systems. The systems under consideration involve time delays in the state and parameter uncertainties. The parameter uncertainties are assumed to be time-varying and norm bounded. New Lyapunov–Krasovskii functional is constructed to derive some delay dependent stability criteria. The proposed methods give both sufficient and necessary and sufficient stability
conditions. Numerical examples have been worked out to show the applicability of the derived results.
Ključne reči:
Discrete-time fractional order systems / discrete time-delay systems / stability / robust stability / Lyapunov functional / delay-independent stability / delay-dependent stabilityIzvor:
Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, 2014, 67-87Izdavač:
- WSEAS Press
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- Održivost i unapređenje mašinskih sistema u energetici i transportu primenom forenzičkog inženjerstva, eko i robust dizajna (RS-MESTD-Technological Development (TD or TR)-35006)
- Razvoj novih metoda i tehnika za ranu dijagnostiku kancera grlića materice, debelog creva, usne duplje i melanoma na bazi digitalne slike i ekscitaciono-emisionih spektara u vidljivom i infracrvenom domenu (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-41006)
- Povećanje energetske efikasnosti HE i TE EPS-a razvojem tehnologije i uređaja energetske elektronike za regulaciju i automatizaciju (RS-MESTD-Technological Development (TD or TR)-33020)
- Dinamika hibridnih sistema složenih struktura. Mehanika materijala (RS-MESTD-Basic Research (BR or ON)-174001)
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Institucija/grupa
Mašinski fakultetTY - CHAP AU - Stojanović, Sreten AU - Debeljković, Dragutin AU - Lazarević, Mihailo PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6685 AB - In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular class of linear discrete time-delay systems are derived. These results are modified and used for checking the stability of discrete-time fractional order systems. The systems under consideration involve time delays in the state and parameter uncertainties. The parameter uncertainties are assumed to be time-varying and norm bounded. New Lyapunov–Krasovskii functional is constructed to derive some delay dependent stability criteria. The proposed methods give both sufficient and necessary and sufficient stability conditions. Numerical examples have been worked out to show the applicability of the derived results. PB - WSEAS Press T2 - Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling T1 - Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems EP - 87 SP - 67 UR - https://hdl.handle.net/21.15107/rcub_machinery_6685 ER -
@inbook{ author = "Stojanović, Sreten and Debeljković, Dragutin and Lazarević, Mihailo", year = "2014", abstract = "In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular class of linear discrete time-delay systems are derived. These results are modified and used for checking the stability of discrete-time fractional order systems. The systems under consideration involve time delays in the state and parameter uncertainties. The parameter uncertainties are assumed to be time-varying and norm bounded. New Lyapunov–Krasovskii functional is constructed to derive some delay dependent stability criteria. The proposed methods give both sufficient and necessary and sufficient stability conditions. Numerical examples have been worked out to show the applicability of the derived results.", publisher = "WSEAS Press", journal = "Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling", booktitle = "Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems", pages = "87-67", url = "https://hdl.handle.net/21.15107/rcub_machinery_6685" }
Stojanović, S., Debeljković, D.,& Lazarević, M.. (2014). Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems. in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling WSEAS Press., 67-87. https://hdl.handle.net/21.15107/rcub_machinery_6685
Stojanović S, Debeljković D, Lazarević M. Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems. in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling. 2014;:67-87. https://hdl.handle.net/21.15107/rcub_machinery_6685 .
Stojanović, Sreten, Debeljković, Dragutin, Lazarević, Mihailo, "Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems" in Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling (2014):67-87, https://hdl.handle.net/21.15107/rcub_machinery_6685 .
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