Robust controller and observer design for time-delay systems

This paper sets forth controller and observer design for a class of uncertain time delay systems. A linear feedback control is first designed to asymptotically stabilize the system assuming full availability of system states. Two Luenberger-like observers are then designed to estimate the system states. Delay-independent sufficient conditions are given, as functions of system parameter uncertainties, for the existence of an observer-controller design to quadratically stabilize the estimation error and preserve the asymptotic stability of the system states. The conditions are given as linear matrix inequalities (LMIs). A numerical example with simulations demonstrates the validity of the approach.