Solvability and Stability of Switched Discrete-time Singular Systems with the Same Switching Rules in Coefficient Matrices

Abstract

The aim of this paper 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 solution manifold. Secondly, by utilizing a Lyapunov function, we derive certain conditions that guarantee the stability of these systems. Finally, we illustrate our results with an example.