Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

Abstract This paper considers the problem of adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.