Delay Dependent Output Feedback Control

Abstract

This chapter considers complex control systems with time-delay under the assumption that the time-delay is precisely known. A Lyapunov–Razumikhin approach is employed to deal with time-delay throughout this chapter. All the developed results consider time-varying delay and there is no limitation on the rate of change of time-delay. This is in contrast with the Lyapunov–Krasovskii approach. Since the time-delay is precisely known, it can be used in both the controller and observer design, and the developed results have high robustness. Both static and dynamical output feedback control schemes are presented for complex time-delay systems. In addition, decentralised static output feedback sliding mode controllers are designed to stabilise a class of complex interconnected time-delay systems where delay exists in both the interconnections and the isolated subsystems. Numerical examples and a case study of river pollution control are provided to demonstrate the developed results.