A T–S Fuzzy Approach to the Local Stabilization of Nonlinear Discrete-Time Systems Subject to Energy-Bounded Disturbances

摘要

This paper addresses the local stabilization problem of nonlinear discrete-time systems subject to energy-bounded disturbances by means of T–S fuzzy models. A fuzzy state feedback controller is designed such that the input-to-state stability in the (ell _2) sense of the original nonlinear system is guaranteed in a bounded region of the state space. Such a region is related to the exactness of the T–S model and describes the domain around the origin where the convexity property remains valid. In addition, an estimate of the closed-loop reachable set is provided for a given class of (ell _2) disturbances. Three (convex) optimization problems are proposed to either minimize the estimate of the reachable set, improve the disturbance tolerance or minimize the (ell _2)-gain from the disturbance input to the regulated output. Numerical examples are considered to illustrate the approach demonstrating the effectiveness of the proposed technique for the control synthesis of nonlinear discrete-time systems...