Further studies on relaxed stabilization conditions for discrete-time two-dimension Takagi–Sugeno fuzzy systems

This paper investigates the stabilization problem of discrete-time two-dimension (2-D) Takagi–Sugeno (T–S) fuzzy systems. Based on a novel non-parallel distributed compensation (non-PDC) control scheme combined with a new non-quadratic Lyapunov function, less conservative stabilization conditions are developed. The proposed non-quadratic Lyapunov function is homogeneous polynomially parameter-dependent on membership functions. As the degree of the Lyapunov function increases, the conservatism of the obtained stabilization conditions is gradually reduced. By exploiting the algebraic property of membership functions, the stabilization conditions approach to exactness in the sense of convergence. Compared with the existing methods, no slack variables are introduced in control synthesis, and hence the same or less conservative results can be obtained with a lower computational cost. A numerical example is given to illustrate the effectiveness of the proposed method.