Solvability and stability of switched discrete-time linear singular systems under Lipschitz perturbations

Abstract

In this paper, the problem of solvability and stability for switched discrete-time linear singular (SDLS) systems under Lipschitz perturbations is studied. By definition of SDLS systems of index-1, we first prove the unique existence of solution of SDLS systems under Lipschitz perturbations with different switching rules on two sides. A variation of constants formula of solution is given and the solution manifold is also described. Secondly, we derive some conditions for stability, asymptotical stability and exponential stability of these systems. Finally, some examples are given to illustrate the obtained results.