Local stabilization of discrete-time T-S fuzzy systems with magnitude- and energy-bounded disturbances

Abstract

Recently, the local stability and local stabilization problems have been investigated by several authors for nonlinear systems described by Takagi-Sugeno (T-S) fuzzy systems. In this paper, we study the local stabilization problem for discrete-time T-S fuzzy systems with magnitude- and energy-bounded disturbances. The control design problem is cast as a linear matrix inequality (LMI) optimization. The state-feedback controller is designed in such a way that, if the initial state is within a certain domain, then the state trajectories under bounded disturbances will not escape the fuzzy modelling region of the state space. Finally, examples. are given to demonstrate the validity of the proposed method.