An LMI approach to H∞ control for linear delay systems

This paper presents an H^∞ controller design method for linear systems with delay states, inputs, and measurement outputs. Using a Lyapunov functional, the stability for delay systems is discussed independently of time delays. A sufficient condition for the existence of H^∞ controllers of any order is given in terms of three linear matrix inequalities (LMIs). Based on the positive definite solutions of their LMIs, we explain briefly how to construct the H_∞ controller which stabilizes time delay systems independently of delays and guarantees an H^∞ norm bound