LMI-Based Design of Fuzzy Controller and Fuzzy Observer for Takagi-Sugeno Fuzzy Systems: New Non-Quadratic Stability Approach

摘要

This paper deals with design procedures of fuzzy controller and fuzzy observer, one of the most important and basic concepts for fuzzy control system design. Fuzzy controller guarantees stability of the whole system i.e. fuzzy controller and fuzzy observer by the Lyapunov stability approach, while fuzzy observer estimates states of the fuzzy dynamic plants. The two designs are formulated as two separate LMI feasibility problems using new non-quadratic stability conditions based on non-quadratic Lyapunov function and Parallel distributed Compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. Then a separation property based on a vector comparison principle is applied to check the stability of the whole system. Whereas, the obtained results are less conservative. Finally, numerical examples are presented to illustrate the effectiveness of our proposal by showing very satisfactory results.