Extensions of weak-invariance principle for nonlinear switched systems with time-invariant and time-varying subsystems

This paper addresses the stability problem for nonlinear switched systems with both time-invariant and time-varying subsystems. Given that Lyapunov-like functions are difficult to construct for nonlinear switched systems, generalized invariance principles are established based on observer functions. For nonlinear switched systems where the subsystems share Lyapunov-like functions, the generalized invariance principles can be specialized to Lyapunov-based invariance principles, where accurate convergent region can be obtained. In addition to the above efforts, the definitions of p-limit system and limit system set are presented, under which the proposed invariance principles are extended to nonlinear switched systems with time-varying subsystems. Illustrative examples show the effectiveness of the theoretical results.