Stability Analysis and Controller Design for Interval Type-2 T-S Fuzzy Systems Based on Interval Type-2 T-S Fuzzy Observer Under non-Parallel Distributed Compensation and Fuzzy Lyapunov Function Approach

In this paper, we investigate the design method for interval type-2 (IT2) T-S fuzzy controller based on IT2 T-S fuzzy observer for nonlinear systems along with uncertainty parameters. In order to analyze the stability and synthesis the control methods conveniently, an IT2 (T–S) fuzzy model is applied through representing the dynamic of nonlinear systems and dynamic of observer. Uncertainty parameters are captured by IT2 membership function characterized by the lower and upper membership functions. In this paper, for IT2 fuzzy controller, the membership functions and number of rules can be freely chosen different from the IT2 T–S fuzzy model and IT2 T-S fuzzy observer. This method is known non- Parallel Distributed Compensation. To reduce the conservativeness of stability analysis, a fuzzy Lyapunov function candidate is applied. The stability conditions in term of linear matrix inequlities (LMIs) are obtained