Stability Analysis and Controller Design for Fuzzy Parameter Varying Systems Based on Fuzzy Lyapunov Function

The fuzzy parameter varying (FPV) system is a mathematical model proposed to handle nonlinear time-varying dynamical systems encountered in engineering, which has some essential advantages in handling time-varying models. In this article, a new relaxation approach is proposed for the analysis and controller design of the FPV system. Different from the current results on the FPV system, the proposed approach employs the fuzzy Lyapunov function and full block S-procedure to reduce the conservatism in analysis. Furthermore, the relaxation technique proposed in this article can be also used in solving controller synthesis problem effectively. As a result, a design procedure of non-PDC output feedback gain-scheduling controller is provided to ensure asymptotic stability of the closed-loop FPV system. A numerical example is provided to illustrate the proposed method.