Robust Delay-dependent Stability of Nonlinear Stochastic Systems Subject to Passivity Performance

• Published in: International journal of control, automation, and systems Vol. 23; no. 3; pp. 692 - 703
• Main Authors: Sun, Chein-Chung, Huang, Ping-Tzan, Ku, Cheung-Chieh, Huang, Kuan-Wei
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.03.2025; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Control; Control systems design; Engineering; Fuzzy control; Liapunov functions; Matrices (mathematics); Mechatronics; Nonlinear systems; Regular Papers; Robotics; Robustness (mathematics); Stability criteria; Stochastic systems; Time lag; 제어계측공학; passivity; multiplicative noise; Fuzzy Lyapunov-Krasovskii function; PDC; T-S fuzzy system
• ISSN: 2005-4092; 1598-6446; 2005-4092
• DOI: 10.1007/s12555-023-0666-2

The delay-dependent stability issue of nonlinear stochastic systems with external disturbance is investigated in this paper subject to passivity performance. Based on the Takagi-Sugeno (T-S) fuzzy model, the Itô formula and Lyapunov function are directly applied to discuss the stability issue. And, some perturbations are considered to represent the uncertainty for discussing the robustness. Moreover, the interval time-varying case represents the time delay effect on the system. A novel Lyapunov function is proposed to develop the stability criterion with the composing fuzzy positive definite matrix for reducing conservatism. Furthermore, a free-matrix-based inequality is employed to introduce some variables for increasing the freedom of calculation. Based on the proposed criterion, the less conservative delay-dependent stability criterion is applied to design a fuzzy controller such that the nonlinear stochastic system is robust asymptotically stable and passive in the mean square. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed design method.