LMI-based Stability and Performance Design of Fuzzy Control Systems: Fuzzy Models and Controllers with Different Premises

This paper presents the stability analysis of the fuzzy control systems based on the fuzzy-model-based approach. The fuzzy controller, which does not require sharing the same premises as those of the fuzzy model, is considered. The class of fuzzy controllers offers the design flexibility and robustness property to the fuzzy control systems. However, conservative stability results will usually be produced compared with the fuzzy control systems with fuzzy controllers sharing the same premises as the fuzzy models. Relaxed LMI-based stability conditions will be derived for this class of fuzzy control systems. Furthermore, LMI-based performance conditions will be given to guarantee the system performance. Numerical examples will be given to illustrate the merits of the proposed approach.