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

• Published in: International journal of control, automation, and systems Vol. 18; no. 11; pp. 2818 - 2829
• Main Authors: Santos, Omar, Ramírez, Miguel, Cuvas, Carlos, Rodríguez-Guerrero, Liliam, Romero, Hugo, Ordaz, Patricio
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.11.2020; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Algorithms; Control; Control theory; Dynamic programming; Engineering; Linear matrix inequalities; Mathematical analysis; Mechatronics; Optimal control; Robotics; Robust control; Stabilization; Time delay systems; 제어계측공학; Robust control; time delay systems; UUB-stability
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-019-0210-6

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.