Stability and Stabilization for Fuzzy Systems With Time Delay by Applying Polynomial Membership Function and Iteration Algorithm

Recently, a switching method is applied to deal with the membership function-dependent Lyapunov–Krasovskii functional (LKF) for fuzzy systems with time delay; however, the Lyapunov matrices are only linear dependent on the grades of membership which leads to linear switching (Wang and Lam, 2019). In this article, the linear dependence on the grades of membership is extended to homogenous polynomially membership function dependent (HPMFD) and the linear switching is extended to polynomial matrix switching, based on which the obtained result contains the previous one as a special case. Furthermore, in order to fully use the introduced variables without speial structure, an iteration algorithm is designed to construct the switching controller and the initial condition of the algorithm is also discussed. The final simulation demonstrates the effectiveness of the developed new results.