H$\infty$ Control for Linear Systems with Time-Varying Delayed States, Control Inputs, and Measurement Outputs

This paper presents an H$\infty$ controller design method for linear systems with time-varying delayed states, inputs, and measurement outputs. Using a Lyapounov unctional , the stability for delay systems is discussed independently of time delays . And a sufficient condition for the existence of H$\infty$ controllers of n-th order is given in terms of three matrix inequalities. Based on the positive-definite solutions of their matrix inequalities, we briefly explain how to construct H$\infty$ construct H$\infty$ controller, which stabilizes time-delay systems independently of delays and guarantees an H$\infty$ norm bound.