Sufficient conditions for Lyapunov's global stability of time-varying hybrid linear systems

Abstract

This paper deals with the derivation of sufficient conditions for global stability and global exponential stability, for any bounded initial conditions in the whole state space, of time-varying hybrid systems by using Lyapunov's second method. In general, those systems consist of coupled analogue and digital substates. The proofs of global stability are based on guaranteeing firstly that the uncoupled analogue and digital substates are stable (or exponentially stable ), and then the couplings between both substates are sufficiently weak to maintain the global stability properties.