The Parameterization of All Stabilizing Modified Repetitive Controllers for Multiple-Input/Multiple-Output Plants

Abstract

In this paper, we give the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants. The basic idea to obtain the parameterization of all stabilizing modified repetitive controllers for multiple-input/multipleoutput plants is very simple. If the modified repetitive controller stabilizes the plant, then the modified repetitive controller must be included in the class of all stabilizing controllers for the plant. The parameterization of all stabilizing controllers for the plant, which is not necessarily modified repetitive controllers, is obtained using the method by Youla et al. and Vidyasagar. The parameterization of all stabilizing controllers includes free parameter, which is stable. Stabilizing modified repetitive controllers for multiple-input/multiple-output systems can be designed using the free parameter in the parameterization. Using this idea, we obtain the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants.