Quadratic stability analysis of fuzzy control systems using stepwise membership functions

• Published in: 2009 IEEE International Conference on Fuzzy Systems pp. 790 - 795
• Main Authors: Lam, H.K., Narimani, M., Seneviratne, L.D.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.08.2009
• Subjects: Control system synthesis; Control systems; Cost function; Educational institutions; Fuzzy control; Fuzzy systems; Linear matrix inequalities; Nonlinear control systems; Power system modeling; Stability analysis
• ISBN: 9781424435968; 142443596X
• ISSN: 1098-7584
• DOI: 10.1109/FUZZY.2009.5277358

This paper presents the stability analysis of fuzzy-model-based control systems. Stepwise membership functions are introduced to facilitate the stability analysis. Through the stepwise 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 are derived in a simple and easy-to-understand manner to guarantee the system stability. The proposed stability analysis approach offers a nice property to include the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated fuzzy-model-based control system. Furthermore, the proposed stability analysis approach can be applied to the fuzzy-model-based control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same. Greater design flexibility is allowed by choosing 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 example is given to illustrate the merits of the proposed approach.