Solvability and Stability of Switched Discrete-time Singular Systems with the Same Switching Rules in Coefficient Matrices
Main Article Content
Abstract
The aim of this work is to study the problem of solvability and stability for switched discrete-time linear singular (SDLS) systems with the same switching rules in coefficient matrices under Lipschitz perturbation. Firstly, we prove the unique existence of the solution, as well as describe the manifold solution. Secondly, by utilizing a Lyapunov function, we derive certain conditions that guarantee the stability of these systems. Finally, we illustrate obtained results through an example.
Keywords:
SDLS systems, index, solvability, stability, Lipschitz perturbation.
References
[1] Y. Xia, J. Zhang, E. Boukas, Control for Discrete Singular Hybrid Systems, Automatica, 2008, Vol. 44,
pp. 2635-2641.
[2] G. Zhai, X. Xu, A Unified Approach to Stability Analysis of Switched Linear Descriptor Systems Under Arbitrary Switching, Int. J. Appl. Math. Comput. Sci., 2010, Vol. 20, No. 2, pp. 249-259.
[3] P. K. Anh, P. T. Linh, Stability of Periodically Switched Discrete-Time Linear Singular Systems, Journal of Difference Equations and Applications, Vol. 23, No. 10, 2017, pp. 1680-1693.
[4] P. K. Anh, P. T. Linh, D. D. Thuan, S. Trenn, The One-step-map for Switched Singular Systems in Discrete-Time, In Proc, 58th IEEE conf, Decision Control, 2019, pp. 605-610.
[5] P. K. Anh, P. T. Linh, D. D. Thuan, S. Trenn, Stability Analysis for Switched Discrete-Time Linear Singular Systems, Automatica, Vol. 119, 2020, pp. 1-9, article 109100.
[6] D. D. Thuan, N. T. Thu, Solvability and Stability of Switched Discrete-time Linear Singular Systems Under Lipschitz Perturbations, J. Difference Equ. Appl., Published Online: 08 April 2024.
[7] P. K. Anh, D. S. Hoang, Stability of a Class of Singular Difference Equations, International Journal of Difference Equations, Vol. 1, No. 2, 2006, pp. 181-193.
pp. 2635-2641.
[2] G. Zhai, X. Xu, A Unified Approach to Stability Analysis of Switched Linear Descriptor Systems Under Arbitrary Switching, Int. J. Appl. Math. Comput. Sci., 2010, Vol. 20, No. 2, pp. 249-259.
[3] P. K. Anh, P. T. Linh, Stability of Periodically Switched Discrete-Time Linear Singular Systems, Journal of Difference Equations and Applications, Vol. 23, No. 10, 2017, pp. 1680-1693.
[4] P. K. Anh, P. T. Linh, D. D. Thuan, S. Trenn, The One-step-map for Switched Singular Systems in Discrete-Time, In Proc, 58th IEEE conf, Decision Control, 2019, pp. 605-610.
[5] P. K. Anh, P. T. Linh, D. D. Thuan, S. Trenn, Stability Analysis for Switched Discrete-Time Linear Singular Systems, Automatica, Vol. 119, 2020, pp. 1-9, article 109100.
[6] D. D. Thuan, N. T. Thu, Solvability and Stability of Switched Discrete-time Linear Singular Systems Under Lipschitz Perturbations, J. Difference Equ. Appl., Published Online: 08 April 2024.
[7] P. K. Anh, D. S. Hoang, Stability of a Class of Singular Difference Equations, International Journal of Difference Equations, Vol. 1, No. 2, 2006, pp. 181-193.