Quadratic-Stability Analysis of Fuzzy-Model-Based Control Systems Using Staircase Membership Functions

• Published in: IEEE transactions on fuzzy systems Vol. 18; no. 1; pp. 125 - 137
• Main Authors: Lam, H.K., Narimani, M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2010; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Communication system control; Control system analysis; Control system synthesis; Control systems; Controllers; Fuzzy; Fuzzy control; Fuzzy logic; Fuzzy set theory; Fuzzy systems; Linear matrix inequalities; linear-matrix inequality (LMI); Mathematical models; Power system modeling; Sliding mode control; Stability analysis; staircase membership functions; Staircases; Studies; Systems stability; Takagi-Sugeno (T-S) fuzzy model
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2009.2037744

This paper presents the stability analysis of fuzzy-model-based (FMB) control systems. Staircase membership functions are introduced to facilitate the stability analysis. Through the staircase membership functions approximating those of the fuzzy model and fuzzy controller, the information of the membership functions can be brought into the stability analysis. Based on the Lyapunov-stability theory, stability conditions in terms of linear-matrix inequalities (LMIs) are derived in a simple and easy-to-understand manner to guarantee the system stability. The proposed stability-analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated FMB control system. Furthermore, the proposed stability-analysis approach can be applied to the FMB control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same. Greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers. By employing membership functions with simple structure, it is possible to lower the structural complexity and the implementation cost. Simulation examples are given to illustrate the merits of the proposed approach.