Finite Time Input to State Stability and Optimization of Switched Nonlinear Systems

Abstract

In this paper, we address the (uniform) finitetime inputtostate stability problem for switched nonlinear systems. We prove that a switched nonlinear system has a useful finitetime inputtostate stability property under average dwelltime switching signals if each constituent subsystem has finitetime inputtostate stability. Moreover, we prove the equivalence between the optimal costs for the switched nonlinear systems and for the relaxed differential inclusion.