The class of all stabilizable time-delay plants with feedback connection by real rational controllers

One of the problems involved in the control of the real system is the time-delay of the control system. The time-delay generally makes the transfer function have an infinite number of poles, then it makes to guarantee the stability of time-delay control system and to specify the control characteristics difficult. One of the ways to overcome this problem is to use the modified Smith predictor. The modified Smith predictor is the controller including the model of time-delay plant, and this makes to guarantee the stability of time-delay control system and to specify the control characteristics easily. However, the modified Smith predictor is an irrational controller. That is, the modified Smith predictor also has infinite number of poles. This causes that the controller design becomes very difficult. In addition, the designed controller is generally very high order, then the design cost becomes expensive. From these reasons, it is desirable both to stabilize the time-delay control system and to make the transfer function have a finite number of poles, by using rational controllers. In this paper, we clarify the class of all stabilizable time-delay plants with feedback connection by real rational controllers.