On the Design of an Observer-Based Controller for Linear Systems with Unknown Delay

Abstract

In this paper, we present two alternative observer-based H∞, control design methods for linear dynamic systems with unknown delay, the later is assumed to evolve in a pre-specified interval. Based on the Lyapunov-Krasovskii functional and some algebraic manipulations, we design observer-based control laws that guarantee the asymptotic stability of the closed-loop control system and the estimation errors. The obtained results are given in terms of linear matrix inequalities. The theoretical claims and the methods reliability are clearly illustrated via two simple examples.