Non-fragile guaranteed cost robust control for discrete uncertain nonlinear systems with time delay

Abstract

To a class of uncertain nonlinear discrete time delay systems, this paper considers the problem of nonfragile guaranteed-cost H∞ controller design method. First, based on the stability criterion and linear matrix inequalities (LMIs) theory, a sufficient condition of the existence of the non-fragile guaranteed-cost H∞ controller is established. Then the problem of control is solved via a robust controller with gain additive and multiplicative perturbations, the designed controller guarantees that the closed-loop system is regular, impulse free and asymptotically stable for all admissible uncertainties and nonlinear element, and satisfies a cost bound, more over, also satisfies H∞ performance index. A numerical example demonstrates that the systems are robust and the design method is effective.