Stabilizing switched systems under a class of restricted switching signals

Abstract

This paper deals with stability of continuoustime switched nonlinear systems whose switching signals obey pre-specified restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems. Given a family of systems, possibly containing unstable dynamics, and the restrictions on the set of admissible switching signals, we identify a class of switching signals that obeys these restrictions and preserves input/output-to-state stability (IOSS) of the resulting switched system. The primary apparatus for our analysis is multiple Lyapunov-like functions. Input-to-state stability (ISS) and global asymptotic stability (GAS) of switched systems under pre-specified restrictions on switching signals are special cases of our results when no outputs (resp., also inputs) are considered.