Multichannel controller synthesis for the plant with three input and two output channels using polynomial matrix decomposition

When applying polynomial methods for the synthesis of multichannel controllers, there is a need for polynomial matrix calculus. However, when using this method, plants with the number of output channels equal to the number of input channels are mainly considered. This is necessary for the convenience of solving a system of linear algebraic equations in a matrix polynomial calculation. A fairly large number of real technical systems have an unequal number of input and output channels. At the same time, the issue of the synthesis of controllers by the polynomial method for multi-channel plants with an unequal number of input and output effects is not worked out in depth enough. In this paper, we consider an example of a linear model of an unstable plant consisting of three standard links with three channels for the input action and two channels for the output action. It is necessary to achieve certain quality indicators of the output vector value, while the control is carried out in the feedback of the system and is summed up with the input action. The plant feature is to limit the task to the second output, since it is essentially a derivative of the first output. The plant was represented as a left - hand polynomial matrix fractional description, and the controller was represented as a right-hand one. For the formation of the characteristic matrix of a closed system, with this variant of the plant and controller decomposition, some structural system transformations are demonstrated. The plant simplicity under consideration is related to the convenience of demonstrating a polynomial synthesis method for such a plants class.