Output feedback stabilization of linear time-delay systems

Abstract

This paper considers the problem of output feedback stabilization of continuous time linear systems with a constant time-delay in the state. We develop a delay-dependent method, which is based on linear matrix inequalities, for designing linear dynamic output feedback controllers which ensure global uniform asymptotic stability for any time-delay not larger than a given bound. We also consider the problem of delay-dependent robust stabilization via output feedback for state-delayed systems with norm-bounded parameter uncertainty. In this situation, the solution is given in terms of a generalized eigenvalue problem. The developed stabilization methods can be implemented numerically very efficiently using existing convex and quasi-convex optimization techniques.