Observer-Based Robust Fuzzy Controller Design for Uncertain Singular Fuzzy Systems Subject to Passivity Criterion

• Published in: Machines (Basel) Vol. 11; no. 2; p. 280
• Main Authors: Chang, Wen-Jer, Huang, Yu-Min, Ku, Cheung-Chieh, Du, Jialu
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.02.2023
• Subjects: Algorithms; Computational geometry; Control systems design; Controllers; Convexity; Design techniques; Fuzzy control; Fuzzy sets; Fuzzy systems; Liapunov functions; Linear matrix inequalities; Mathematical analysis; Mathematical optimization; Nonlinear systems; observer-based fuzzy control; Optimization; passivity performance constraint; Proportional derivative; proportional derivative control; Robust control; Singular value decomposition; Takagi–Sugeno fuzzy systems
• ISSN: 2075-1702; 2075-1702
• DOI: 10.3390/machines11020280

This paper discusses an observer-based control problem for uncertain Takagi–Sugeno Fuzzy Singular Systems (T-SFSS) subject to passivity performance constraints. Through the Parallel Distributed Compensation (PDC) approach and the Proportional Derivative (PD) control scheme, an observer-based fuzzy controller is constructed to achieve the stability of the considered system. An unlimited positive definite matrix is utilized to construct the Lyapunov function and derive sufficient stability conditions to develop a relaxed design method. Moreover, some technologies, such as the Schur complement, projection lemma, and Singular Value Decomposition (SVD), are applied to convert the conditions to Linear Matrix Inequality (LMI) form. Therefore, the convex optimization algorithm is used to solve the LMI conditions to find feasible solutions. The observer-based fuzzy controller is established with the obtained solutions to guarantee stability and passivity performance for the uncertain nonlinear singular systems. Finally, two examples are provided to verify the availability of the proposed fuzzy control approach.