On the Ultimate Uniform Bounded-stabilization for a Class of Perturbed Time Delay System via Sub-optimal Robust Control

This paper deals with the robust control design for a class of time delay systems subject to unmatched disturbances and/or uncertain dynamics. For this, a specific Lyapunov-Krasovskii functional, the so called Attractive Ellipsoid concept and the dynamic programming algorithm for optimal control, are summarized to design the sub-optimal robust control law. Thus, the Lyapunov-Krasovskii candidate functional associated with specific Linear Matrix Inequality solution is aimed to guarantee the so called Ultimate Uniform Bounded-Stabilization. Furthermore, the sub-optimal robust control is achieved by minimizing a Hamilton-Jacobi-Bellman like equation, related to Lyapunov-Krasovskii type functional, respect to the admissible control. Hence, the robust and exponential stabilization is concluded for a perturbed and unperturbed time delay system, respectively. The theoretical results are illustrated on two numerical systems.