Further Studies on Control Synthesis of Discrete-Time T–S Fuzzy Systems via Useful Matrix Equalities

This paper is concerned with further studies on the control synthesis of discrete-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy form. To do this, a novel slack variable technique is presented by developing some useful matrix equalities, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected for the first time into sets of united collection matrices. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved, i.e., the convergence of asymptotically necessary and sufficient stabilization conditions is further sped up. Finally, a numerical example is provided to illustrate the effectiveness of the proposed result.