Practical Stability of Switched Systems With Multiple Equilibria Under Disturbances

Abstract

Our objective in this paper is to establish robustness to disturbances for continuous-time switched systems with multiple equilibria (SSME) while being unaware of the disturbances. We provide an average dwell-time bound which can be computed without explicit knowledge of the disturbance. Switching signals that satisfy this bound ensure safe operation of the switched system for sufficiently small disturbances by the notion of practical stability. In essence, this paper establishes the robustness property that safe evolution of the SSME in the absence of disturbances results in the safety of the SSME under mild disturbances. Our motivation for studying SSMEs under disturbances arises from robotics, where certain motion planning problems require switching among controllers under unknown or unmodeled disturbances. However, these results are applicable to a much broader class of applications.