On stability of solutions for a class of nonlinear difference systems with switching

The stability of the trivial solution for a class of difference systems with switching and sector‐type nonlinearities is studied. Different approaches to common Lyapunov function design for the family of subsystems corresponding to the considered switched system are proposed. Sufficient conditions making the trivial solution asymptotically stable for any switching law are determined. In the case when common Lyapunov function design fails, multiple Lyapunov functions are used to obtain the restrictions on the switching law guaranteeing the asymptotic stability of the trivial solution.