Novel Delay-Dependent Stabilization for Fuzzy Stochastic Systems with Multiplicative Noise Subject to Passivity Constraint

• Published in: Processes Vol. 9; no. 8; p. 1445
• Main Authors: Ku, Cheung-Chieh, Chang, Wen-Jer, Huang, Kuan-Wei
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2021
• Subjects: Algorithms; Automatic pilots; Closed loop systems; Computational geometry; Control systems design; Controllers; Convexity; Delay; Derivatives; Design techniques; Fuzzy control; Fuzzy sets; Fuzzy systems; Linear matrix inequalities; Mathematical analysis; Noise; Optimization; Passivity; Stability criteria; Stabilization; Stochastic systems; Time varying control
• ISSN: 2227-9717; 2227-9717
• DOI: 10.3390/pr9081445

A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.