Stabilizing switched nonlinear systems under restricted but arbitrary switching signals
Atreyee Kundu
TL;DR
This work addresses IOSS for continuous-time switched nonlinear systems under pre-specified restrictions on admissible switches and dwell times. It develops a graph-theoretic framework with multiple IOSS-Lyapunov-like functions and a weighted directed graph, introducing contractive and jointly contractive walks to certify IOSS for all admissible switching signals. The main contribution is a sufficient-condition theorem that guarantees IOSS under restricted switching, together with practical, numerically tractable criteria to verify contractivity through simple walks and cycles. The results extend stability analysis to broad classes of switching signals encountered in engineering, enabling robust state estimation and control design for switched nonlinear dynamics. The numerical example demonstrates the approach on a three-subsystem system, illustrating how dwell-time and switch constraints translate into contractive graph walks and guaranteed stability.
Abstract
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.