An Approach for Stability Analysis of Polynomial Fuzzy Model-Based Control Systems

Stability analysis of polynomial fuzzy model-based (PFMB) control systems under the parallel distributed compensation (PDC) design technique is investigated. A new polynomial fuzzy controller (PFC) is introduced to release conservativeness in the existing approaches. Compared to the conventional (PFC), the controller under consideration in this paper has a favorable property which introduces some more variables in the stability conditions such that, the solution of the derived stability conditions can be explored in a larger group of potential solutions. This property may lead to further relax stability conditions. However, the stability conditions will not be in the form of SOS conditions. Hence, particle swarm optimization (PSO) is employed to explore the solution of the derived stability conditions which are in the form of state-dependent BMI. It is shown that the conventional PFC is a special case of that of proposed one. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.