Strong stabilization of systems with states and control time delays

Stable controllers are preferable over non-stable ones due to their reliability and implementation. This paper addresses the strong stabilization problem for continuous-time linear systems with an unknown time delay both in states and inputs via static and dynamic output feedback controllers. A new criterion for dynamic output feedback stabilizability is proposed in terms of linear matrix inequality. The formulation will separate the controller parameters and the Lyapunov matrices. The effectiveness and merits of the proposed approach are shown through examples.