Input-to-state robust safety of switched nonlinear systems using multiple barrier functions

Abstract

This paper studies input-to-state robust safety (ISRSf) for switched nonlinear systems, and provides a way to describe and analyze the robustness of systems’ safety with respect to external inputs in the switched systems framework. Without requiring the ISRSf of each subsystem, ISRSf via state-dependent switching law is obtained by exploiting a multiple barrier functions method, and a sufficient condition for ruling out Zeno phenomenon is provided. Moreover, ISRSf of switched cascade-connected systems is achieved by using multiple barrier functions and a designed dual switching law. Finally, two illustrative examples, which include a simple mobile robot navigation with controller switching, are presented to demonstrate the feasibility of the theoretical results.