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

Time delays in the feedback control often dete-riorate the control performance or even cause the instabilityof a dynamic system.This paper presents a control strategyfor the dynamic system with a constant or a slowly time-varying input delay based on a transformation,which sim-plifies the time-delay system into a delay-free one.Firstly,the relation is discussed for two existing reduction-basedlinear quadratic controls.One is continuous and the otheris discrete.By extending the relation,a new reduction-basedcontrol is then developed with a numerical algorithm pre-sented for practical control implementation.The controllersuggested by the proposed method has such a promisingproperty that it can be used for the cases of different values ofan input time delay without redesign of controller.This prop-erty provides the potential for stabilizing the dynamic systemwith a time-varying input delay.Consequently,the applica-tion of the proposed method to the dynamic system with aslowly time-varying delay is discussed.Finally,numericalsimulations are given to show the efficacy and the applica-bility of the method.