Novel stability conditions for discrete-time T–S fuzzy systems: A Kronecker-product approach

This paper is concerned with the issue of developing a novel strategy to reduce the conservatism of stability conditions for discrete-time Takagi–Sugeno (T–S) fuzzy systems. Unlike the previous ones which are almost quadratic with respect to the state vector, a new class of Lyapunov functions is proposed which is quadratic with respect to the Kronecker products of the state vector, thus including almost the existing ones found in the literature as special cases. By combining the characterizations of homogeneous matrix polynomials and the properties of membership functions, relaxed stability conditions are derived in the form of linear matrix inequalities which can be efficiently solved by the convex optimization techniques. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.