Analytical design of Takagi-Sugeno fuzzy control systems

Based on the properties analysis of Takagi-Sugeno (T-S) fuzzy systems with two-overlapped fuzzy partition (TFP) inputs, an analytical design approach of T-S fuzzy control systems is proposed in this paper. This approach includes two parts: (1) a new method to check the stability of a T-S fuzzy control system which only requires to find a common positive-definite matrix in each maximal overlapped-rules group (MORG). This method can reduce the conservatism and difficulty of the former stability analysis methods. (2) The systematic design of T-S fuzzy controllers by means of the parallel distributed compensation (PDC) and linear matrix inequalities (LMI). The simulation results of a nonlinear mass-spring-damper system show that this approach is effective.