On the existence of common Lyapunov triples for ISS and iISS switched systems

Abstract

We present converse Lyapunov theorems for input-to-state (ISS) and integral ISS (iISS) switched nonlinear systems. Their proofs are based on existing converse Lyapunov theorems for input-output-to-state stability and iISS nonlinear systems, and on the association of the switched system with a nonlinear system with inputs and disturbances that take values in a compact set.