Delay Dependent Finite Time Stability of Discrete Time Delay Systems: Towards the New Solution
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.
Keywords:
Solutions / Finite time stability / Discrete time delay systems / Discrete matrix equationsSource:
2015 International Conference on Applied Mechanics and Mechatronics Engineering (Amme 2015), 2015, 228-233Publisher:
- Destech Publications, Inc, Lancaster
Collections
Institution/Community
Mašinski fakultetTY - 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 .