Observer-based Extended Dissipative Control for Delayed Singular Markovian Jump Systems via Relaxed Lyapunov-Krasovskii Functional

• Published in: International journal of control, automation, and systems Vol. 20; no. 12; pp. 3833 - 3848
• Main Authors: Wang, Xin, Zhuang, Guangming, Xia, Jianwei, Chen, Guoliang, Zhang, Huasheng
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.12.2022; Springer Nature B.V
• Subjects: Catalytic cracking; Closed loops; Control; Control systems design; Dissipation; Engineering; Feedback control; Linear matrix inequalities; Mathematical analysis; Mechatronics; Regular Papers; Robotics; State feedback; relaxed Lyapunov-Krasovskii functional; singular systems; Markovian jump systems; memory state feedback controller; Extended dissipative control
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-021-0621-z

This paper addresses the problem of observer-based extended dissipative control for singular Markovian jump systems with time-varying delays. By using relaxed Lyapunov-Krasovskii functional approach and strict linear matrix inequality method, sufficient conditions are proposed to ensure that the delayed singular Markovian jumping system is stochastically admissible and extended dissipative. Based on these conditions, a desired observer-based memory state feedback controller is designed to ensure that the closed-loop system satisfies stochastic admissibility and extended dissipativity. Finally, two examples including a numerical example and an oil catalytic cracking process are provided to illustrate the effectiveness of the proposed methods.