In the present paper, we examine the parameterization of all stabilizing Internal Model Controllers(IMC) for multiple-input/multiple-output unstable plant. The parameterization problem is theproblem in which all stabilizing controllers for a plant are sought [1, 2, 3, 4, 5, 6, 7, 8, 9]. Since this parameterizationcan successfully search for all proper stabilizing controllers, it is used as a tool for manycontrol problems. However, there exists a problem whether or not stabilizing controllers for unstableplant can be represented by IMC structure. The IMC structure has advantages such as closed-loop stabilityis assured simply by choosing a stable IMC parameter. Additionally, closed-loop performancecharacteristics are related directly to controller parameters, which makes on-line tuning of the IMCvery convenient[6]. The solution to this problem, Morari and Zafiriou[6] examined the parameterizationof all stabilizing IMC for unstable plant. Their parameterization remains difficulties. Their internalmodel is not necessarily proper. In addition, their parameterization includes improper IMC. In order toovercome these problems, Chen et al. proposed a design method for IMC for minimum-phase unstableplant[17]. However, the method proposed by Chen et al. cannot apply for multiple-input/multipleoutputunstable plant. Because many of actual plants are multiple-input/multiple-output plants, consideringfor multiple-input/multiple-output unstable plant is important. In this paper, we propose theparameterization of all proper stabilizing IMC for multiple-input/multiple-output unstable plant suchthat the IMC and the internal model are proper. In addition, we present an application of the result forcontroller design for multiple-input/multiple-output time-delay plant.

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The modified Smith predictor is well known as an effective time-delay compensator for a plant with large time-delays, and several papers on the modified Smith predictor have been published. The parameterization of all stabilizing modified Smith predictors for single-input/single-output time-delay plants is obtained by Yamada et al. However, they do not examine the parameterization of all stabilizing modified Smith predictors for multiple-input/multiple-output time-delay plants. The purpose of this paper is to expand the result by Yamada et al. and to propose the parameterization of all stabilizing modified Smith predictors for multiple-input/multiple-output time-delay plants. Control characteristics of the control system using obtained parameterization of all stabilizing modified Smith predictors are also given. Finally, a numerical example is illustrated to show the effectiveness of proposed parameterization of all stabilizing modified Smith predictors.

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