I. Introduction
Multi-coupled control systems are being used more and more in recent years. The advantages of such systems consist in the possibility of autonomous control of each output value of the control obj ect, even in the case when the internal connections between the inputs and outputs of the objects are so strong that the influence at each input affects the output values at each output. Such systems are called MIMO, which means many inputs and many outputs. For the MIMO object, the MIMO controller is also required, in which each control error at any of the outputs affects the change in the control signal at each of the inputs of the object. Earlier, to control such complex objects, the problems of calculating the optimal control for transferring the object from the initial state to the required one were solved; this direction has gradually become obsolete. Now the optimal controller is calculated, that is, such a controller structure that forms the optimal control from the difference between the required vector of the object's outputs and the actual state of its output values. These differences are called control errors, and a typical control system structure is shown in Fig. 1, where all lines denote vector quantities, for example, for a 2 × 2 object, all quantities are 2 × 1 column vectors, and,\begin{align*} & V(s)=[v_{1}1(s)v_{2}(s)]^{T}, \tag{1}\\ & Y(s)=[y_{1}1(s)y_{2}(s)]^{T}, \tag{2}\\ & E(s)=[e_{1}1(s)ve_{2}(s)]^{T}, \tag{3}\\ & U(s)=[u_{1}1(s)u_{2}(s)]^{T}. \tag{4} \end{align*}