An adaptive tracking problem for a family of retarded time‐delay plants

Abstract

Abstract Most of the existing switching control techniques are developed specifically for finite‐dimensional linear time‐invariant (LTI) systems. In many practical applications, however, it is essential to take time delay into consideration in the modelling as the control system can be highly sensitive to delay. In this paper, a multi‐model switching control algorithm is proposed for retarded time‐delay systems. It is assumed that the plant is represented by a family of known multi‐input multi‐output, observable, LTI models with multiple delays in the states, and that corresponding to each model in the known family, there exists a high‐performance finite‐dimensional LTI controller. In addition, it is supposed that a bound on the magnitude of the external inputs and disturbances is available. It is then shown that the proposed switching controller can stabilize the uncertain system, and that under some mild conditions, output tracking can be achieved in the given problem setting. Copyright © 2007 John Wiley & Sons, Ltd.