An LMI Approach to H" Control for Linear Delay Systems

This paper presents an H" controller design method for linear systems with delayed states, inputs, and measurement outputs. Using a Lyapunov functional, the stability for delay systems is discussed independently of time delays. And a sufficient condition for the existence of Ha controllers of any order is given in terms of three linear matrix inequalities(LM1s). Based on the positive definite solutions of their LMIs, we briefly explain how to construct H" controller, which stabilizes time delay systems independently of delays and guarantees an H" norm bound.