The parameterization of all robust stabilizing Internal Model Controllers for multiple-input/multiple-output plants

In the present paper, we examine the parameterization of all robust stabilizing Internal Model Controllers (IMCs) for multiple-input/multiple-output plants with uncertainties. The parameterization problem is the problem in which all stabilizing controllers for a plant are sought. Since this parameterization can successfully search for all proper stabilizing controllers, it is used as a tool for many control problems. For stable plants, the parameterization of all stabilizing controllers can be represented by the IMC structure. The IMC structure has advantages such as closed-loop stability is assured simply by choosing a stable IMC parameter. Additionally, closed-loop performance characteristics are related directly to controller parameters, which make online tuning of the IMC very convenient. However, there exists a question whether or not, stabilizing controllers for unstable plants can be represented by the IMC structure. The solution to this problem, Morari and Zafiriou, Chen et al. and Mai et al. clarified that any stabilizing controller for unstable plants can be represented by the IMC structure by the parameterization of all stabilizing IMCs for unstable plants. However, their IMCs cannot guarantee the stability of control system for plants with uncertainties. In this paper, we clarify the parameterization of all proper robust stabilizing IMCs for multiple-input/multiple-output plants such that the IMC and the internal model are proper.