An LMI approach to H_∞ controller design for linear time-delay systems

We develop an output feedback H_∞ control design method for linear time-delay systems based on the linear-matrix-inequality (LMI) approach. A sufficient condition for the existence of H_∞ controllers of any order is given in terms of three LMIs. The condition is valid for both singular and regular problems. We also give a characterization of H_∞ controllers in state space. The LMI existence condition can be easily determined whether or not, it is feasible and if it is then one can easily obtain H_∞ controller gain matrices via convex optimization.