The Parameterization of All Plants Stabilized by a PID Controller

In this paper, we examine the parameterization of all plants that can be stabilizedby a Proportional–Integral–Derivative (PID) controller. The PID controller structure is themost widely used controller structure in industrial applications. Recently, if stabilizing PIDcontrollers for the plant exist, the parameterization of all stabilizing PID controllers was considered.However, the parameterization of all plants that can be stabilized by a PID controllerhas not been examined. In this paper, we clarify this question. In addition, we present theparameterization of all stabilizing PID controllers for plants that can be stabilized by a PIDcontroller.