Stabilization of discrete-time switched systems with all unstable modes

Stabilization problem for discrete-time switched systems with all unstable modes is investigated in this paper. Following the idea of getting into each unstable mode and analyzing its internal behavior, the state dynamical decomposition technique is used to convert such a problem to an equivalent one for the inter-decoupled switched systems. The proposed mode-dependent average dwell time approach (MDADT) ensures each sub-state switched system is globally exponentially stable. Moreover, a periodical switching law is designed to guarantee the asymptotic stability of discrete-time switched systems. Finally, a numerical example is given to show the validity of the main results.