Predictor-Based Stabilization for Linear Switched Systems with Input Delays

Abstract

This paper investigates the controller design problem for switched systems with input delays. A predictor-based switched controller is proposed to compensate for the effect of input delays. By introducing an appropriate transformation, the switched system with input delays is converted into an equivalent switched partial differential equation system. The exponential stability of the resulting closed-loop system is established by constructing multiple Lyapunov–Krasovskii functionals, which allows for arbitrarily large input delays. Furthermore, the robustness of the proposed controller against perturbations in switching signals is rigorously analyzed based on the Lyapunov–Krasovskii framework. A dynamic predictor-based switched controller is also developed, and the exponential stability of the corresponding closed-loop system is guaranteed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control schemes.