LMI-Based Stability Analysis of Fuzzy-Model-Based Control Systems Using Approximated Polynomial Membership Functions

• Published in: IEEE transactions on systems, man and cybernetics. Part B, Cybernetics Vol. 41; no. 3; pp. 713 - 724
• Main Authors: Narimani, M, Lam, H K, Dilmaghani, R, Wolfe, C
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2011
• Subjects: Algorithms; Approximation; Approximation methods; Artificial Intelligence; Computer Simulation; Control systems; Cybernetics; Derivatives; Feedback; Fuzzy control; Fuzzy Logic; Fuzzy systems; linear matrix inequality (LMI); Lyapunov functions; Mathematical models; membership-function-shape-dependent stability conditions; Models, Statistical; Numerical Analysis, Computer-Assisted; Numerical stability; Polynomials; Shape; Stability; Stability analysis; Takagi-Sugeno (T-S) fuzzy model
• ISSN: 1083-4419; 1941-0492; 1941-0492
• DOI: 10.1109/TSMCB.2010.2086443

Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S -procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.