Analysis and Design for Uncertain Discrete fuzzy System Based on Piecewise Fuzzy Lyapunov Approach

Based on Takagi-Sugeno fuzzy model, this paper adopts the piecewise fuzzy Lyapunov function into the analysis of nonlinear discrete systems with parametric uncertainties. Firstly, a new sufficient condition to check the stability of closed-loop discrete T-S fuzzy systems is proposed after the definition of a discrete piecewise fuzzy Lyapunov function. This condition only needs to satisfy the condition of the fuzzy Lyapunov approach in each maximal overlapped rule group. Therefore, the proposed condition is less conservative and less difficult than the common Lyapunov approach and the fuzzy Lyapunov approach. Then, by using the method of parallel distributed compensation, the stability of the closed-loop discrete T-S fuzzy system is analyzed and the fuzzy controller is designed. Finally, a simulation example shows the approach is effective and advantageous.