Stability Analysis for Interval Type-2 Fuzzy Systems by Applying Homogenous Polynomially Membership Functions Dependent Matrices and Switching Technique

In this article, the homogenous polynomially membership functions dependent (HPMFD) matrices are used to study the interval type-2 Takagi-Sugeno fuzzy systems. First, some necessary notations of the HPMFD matrices are introduced. Next, based on these notations, the time derivative of the HPMFD matrices is discussed and a switching method is proposed to ensure that the time derivative of the HPMFD matrices is negative. Then, a HPMFD controller is designed and new stabilization conditions are obtained by using the HPMFD Lyapunov function. In the end, the simulations show that the method in this article is less conservative than the existing ones in the literatures.