Input-to-state exponential stability of switched nonlinear time-delay systems having stable/unstable subsystems

Abstract

This research introduces new approaches to the Lyapunov–Krasovskii methodology to ensure the input-to-state exponential stability of switched nonlinear time-delay systems with stable and unstable subsystems. New average dwell-time bounds are provided by using the trade-off among the activation times of the stable and unstable subsystems. As illustrative examples, two systems representing neuronal population phenomena with additive and multiplicative inputs are analyzed. As two examples show, these criteria apply to a broad class of switched nonlinear time-delay systems.