H∞-controllers for time-delay systems using linear matrix inequalities

In this paper, H (infinity) -control design is developed for nominally linear systems with input as well as state delays. Both stability and H (infinity) -norm bound conditions are established for asymptotically stable controlled systems. Necessary and sufficient conditions for feedback control synthesis are established first by using two forms; the first has one term representing pure state feedback, and the second has two terms comprising pure state feedback plus delayed state feedback. Then, the corresponding synthesis conditions for the cases of static-output feedback and observer-based feedback controllers are developed. The results are cast conveniently into a linear matrix inequality (LMI) framework, which can be solved numerically by efficient interior-point methods. With the aid of the LMI control toolbox software, the theoretical work is illustrated by computer simulation of numerous examples.