State Feedback Controller Design for General Polynomial-Fuzzy-Model-Based Control Systems

This paper studies state feedback controller design for polynomial-fuzzy-model-based (PFMB) control system, which contains a polynomial fuzzy model (PFM) and a polynomial fuzzy controller (PFC) to show a nonlinear plant. A polynomial Lyapunov function candidate relying on any system states is chosen to prove the PFMB control system that has different membership functions and fuzzy rules between PFM and PFC, which produce more diversification in design and less conservative stability conditions. The provided novel sum of squares (SOS) optimization method is used to solve the nonconvex conditions by describing the nonlinear terms as semidefinite programming (SDP) problem and making the optimal value is zero. To have a better stability analysis, a relaxation matrix that considers the information of the membership function product is proposed. The exported SOS-based conditions combined with Lyapunov stability theorem are added into the stability analysis, which guarantee that the system is stable. The numerical simulation example gives a good proof of the validity of the introduced approach.