Input/output-to-state stability of discrete-time switched nonlinear systems under restricted switching

Abstract

We study input/output-to-state stability (IOSS) of discrete-time switched nonlinear systems. The switching signals obey two types of restrictions: first, transitions between subsystems are restricted, and second, minimum and maximum dwell time on subsystems are restricted. Given a family of systems such that not all systems in the family are IOSS, our objective is to construct a time-dependent switching signal that ensures IOSS of the resulting switched system under the above restrictions. We report that the algorithm proposed in [5] for constructing a stabilizing periodic switching signal for continuous-time switched nonlinear systems, extends to the discrete-time setting under standard assumptions. Multiple Lyapunov-like functions and graph-theoretic tools are the primary apparatuses for our analysis.