STABILITY OF NONLINEAR SWITCHED SYSTEMS WITH TIME DELAY

Abstract

This paper addresses the stability problem of switched nonlinear systems with time delay. The dynamics of the considered system are governed by a switching signal that describes transitions between multiple subsystems, while the effect of time delay is explicitly taken into account. Ensuring system stability under arbitrary switching signals is a challenging and important problem in control theory. In this study, a method based on the Lyapunov-Krasovskii functional is employed to derive sufficient stability conditions for switched nonlinear systems with time delay. The proposed approach allows simultaneous consideration of nonlinear system properties, time-delay effects, and switching behavior, thereby providing a generalization of classical results. In addition, finite-time stabilization conditions are investigated, and a corresponding nonlinear state-feedback control law is proposed. This control law guarantees that the system states converge to the equilibrium within a finite time and achieves faster stabilization compared to asymptotic stability.The obtained theoretical results are validated through numerical simulations. The simulation results demonstrate that the system state variables converge to the equilibrium despite the presence of switching and time delay. Moreover, multiple switchings do not deteriorate system stability. The results confirm the effectiveness of the proposed method and show its applicability to the control of switched nonlinear systems with time delay.