Robust stabilization of linear continuous systems subjected to time-varying state delay and perturbations

In this paper, we address the robust stabilization problem by a memoryless state feedback of linear continuous systems including state time delay and parametric perturbations. Both time delay and parametric perturbations are time-varying and two classes of highly structured and unstructured perturbations are discussed respectively. By making use of the Lyapunov stability approach associated with norm or matrix measure techniques, a new stabilizability criterion and the corresponding memoryless state feedback control laws that guarantee to stabilize the mentioned system are developed. The main feature of the present schemes is that the proposed stabilizability criterion does not involve any matching conditions. Besides defining a family of allowable memoryless state feedback control laws to stabilize the time-delay systems with any one of the two classes of perturbation, it can also determine feedback controllers to guarantee that the closed-loop system have a specified stability degree. Finally, we give a numerical example and computer simulations to confirm the validity and to demonstrate the applicability of the present schemes.