Stability via Hybrid-Event-Time Lyapunov Function and Impulsive Stabilization for Discrete-Time Delayed Switched Systems

This paper proposes a new stability analysis method called the hybrid-event-time Lyapunov function (HTLF) approach for discrete-time delayed switched systems (DDSS). Two types of stability notions (GUAS and event-GUAS) are proposed to reflect the effects on stability from events. A basic stability result is derived: a DDSS has event-GUAS if and only if there exists an HTLF which is strictly decreasing and converges to zero. Moreover, some sufficient conditions expressed by HTLF-Razumikhin-type stability theorems are established. The issue of impulsive stabilization for DDSS is studied. It is proved that an unstable DDSS can be stabilized by impulsive control. And the impulsive stabilization to input-to-state stability of DDSS is also achieved.