Stabilizing switched nonlinear systems under restricted but arbitrary switching signals

This paper deals with input/output-to-state stability (IOSS) of switched nonlinear systems whose switching signals obey pre-specified restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems. We present sufficient conditions on the subsystems, admissible switches between them and admissible dwell times on them, such that a switched system generated under all switching signals obeying the given restrictions is IOSS. Multiple Lyapunov-like functions and graph theory are the key apparatuses for our analysis. A numerical example is presented to demonstrate our results.