A note on input-to-state stability and averaging of fast switching systems

Abstract

We consider the averaging method for stability of rapidly switching nonlinear and linear systems with disturbances. First, we show that the input-to-state stability (ISS) analysis results for continuous-time systems in [7] apply directly to nonlinear rapidly switched systems that we consider. We show that the notions of strong and weak averages that were proposed in [7] play an important role in the context of switched systems. A direct application of results in [7] yields conditions under which ISS of the strong average implies semi-global practical ISS (SGP-ISS) of the switched system. A similar result was shown to hold for weak averages but the conclusion is slightly weaker as we can only..