A new reduction-based LQ control for dynamic systems with a slowly time-varying delay

Time delays in the feedback control often deteriorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly time-varying input delay based on a transformation, which simplifies the time-delay system into a delay-free one. Firstly, the relation is discussed for two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method. The project was supported by the National Natural Science Foundation of China (10532050, 10702024 and 10702025) and the Doctoral Fund of MOE of China (20070287029).