Ultimate Boundedness Control for Uncertain Nonlinear Impulsive Switched Systems: A Fuzzy Approach Based on a Complete Takagi–Sugeno Structure

Abstract

This paper deals with the ultimate boundedness control of nonlinear impulsive switched systems, which ensures that the state trajectories ultimately converge to a sufficient small region containing the origin. Given a general model, we first propose novel stability criteria that do not need to be satisfied on the entire space and include a condition to guarantee the remaining of trajectories within the ultimate bound, even though the impulse size is not zero at the origin or is not vanishing near the origin. Applying these criteria to a closed-loop system leads to a set of matrix inequalities that may be infeasible when the subsystems are highly nonlinear. Therefore, we redevelop them for an impulsive switched system represented by Takagi–Sugeno (T–S) fuzzy structure with nonlinear consequent parts. Since this structure has fewer rules than the traditional T–S models with linear consequent parts, the number of established stabilization matrix inequalities is sharply reduced. We then derive an optimization problem with linear and bilinear constraints to achieve a fuzzy controller that guarantees convergence to the smallest ultimate bound as well as practical control issues. Finally, a numerical example and a practical-motivated example are given to demonstrate the applicability of the proposed approach.