LMI-Based Stability Analysis for Fuzzy-Model-Based Control Systems Using Artificial T-S Fuzzy Model

• Published in: IEEE transactions on fuzzy systems Vol. 19; no. 3; pp. 505 - 513
• Main Author: Lam, H K
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytical models; Asymptotic stability; Control systems; Fuzzy; Fuzzy control; Fuzzy logic; Fuzzy set theory; linear-matrix inequality (LMI); Lyapunov methods; Mathematical models; Numerical stability; Stability; Stability analysis; Stability criteria; staircase membership functions; Staircases; Studies; Takagi-Sugeno (T-S) fuzzy model
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2011.2116027

This paper investigates the stability of fuzzy-model-based (FMB) control systems. An alternative stability-analysis approach using an artificial fuzzy system based on the Lyapunov stability theory is proposed. To facilitate the stability analysis, the continuous membership functions of the Takagi-Sugeno (T-S) fuzzy model are represented by the staircase ones. With the nice property of the staircase membership functions, it turns the set of infinite number of linear-matrix-inequality (LMI) based stability conditions into a finite one. Furthermore, the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions. The stability of the original FMB control systems is guaranteed by the satisfaction of the LMI-based stability conditions. The proposed stability analysis is applied to the FMB control systems of which the T-S fuzzy model and fuzzy controller do not share the same premise membership functions and, thus, is able to enhance the design flexibility of the fuzzy controller. A simulation example is given to illustrate the merits of the proposed approach.