A Fuzzy Lyapunov Function Method to Stability Analysis of Fractional-Order T–S Fuzzy Systems
Xiaofei Fan, Zhanshan Wang
Abstract
This article investigates the stability analysis and stabilization problems for fractional-order T–S fuzzy systems via fuzzy Lyapunov function method. A membership-function-dependent fuzzy Lyapunov function instead of the general quadratic Lyapunov function is employed to obtain the stability and stabilization criteria. Different from the general quadratic Lyapunov function, the fuzzy Lyapunov functions contain the product of three term functions. Since the general Leibniz formula cannot be satisfied for fractional derivative, the current results on the fractional derivative for the quadratic Lyapunov functions cannot be extended to the fuzzy Lyapunov functions. Therefore, to estimate the fractional derivative of fuzzy Lyapunov functions, the fractional derivative rule for the product of three term functions is proposed. Based on the proposed fractional derivative rule, the corresponding stability and stabilization criteria are established, which extend the existing results. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical analysis.