Stability of Nonlinear Hybrid Systems

Abstract

This work is devoted to stability of nonlinear hybrid systems (or nonlinear systems with regime switching). The switching regime is described by a finite-state Markov chain. Both continuous-time and discrete-time systems are considered. Aiming at reduction of complexity, the system is setup as one with two-time scales which gives rise to a limit system as the jump rate of the underlying Markov chain goes to infinity. Using perturbed Liapunov function methods, the stability of the original system in an appropriate sense is obtained provided that the corresponding limit system is stable.