Stability With Safety Analysis for Switched Systems via Multiple Lyapunov and Barrier Functions

Safety and stability are two critical issues in many practical switched control systems, particularly those used in industrial, transportation, medical, and other high-risk applications where failure could lead to serious consequences. This paper is concerned with the issue of proposing sufficient conditions for simultaneously verifying the stability and safety of time-varying switched nonlinear systems (TSNS) under a state-dependent but unsafe-region-independent switching signal. Specifically, based on multiple Lyapunov functions and multiple barrier functions, we at first present several sufficient conditions for simultaneously obtaining the (uniform) stability with safety, (uniform) asymptotic stability with safety, and (uniform) exponential stability with safety of TSNS with any form of unsafe set. Furthermore, considering the broad applications of finite-time stability in practical systems, a sufficient condition for simultaneously achieving finite-time stability and safety is presented. Note that the above conditions relax the requirements of the nonincreasing property of the multiple Lyapunov functions and multiple barrier functions along the trajectories of TSNS. In the end, the effectiveness of our results is illustrated by four examples.