Synthesis of linear multichannel regulators using structural transformations

The paper considers the problem of using left and right matrix polynomial decompositions in the synthesis of regulators using modal method. The left matrix polynomial expansion is assumed. In the synthesis of regulators, the complexity of computations essentially increases when the inequality of the column/row degrees of the polynomial matrix of the "denominator" of the object. After transition from the left matrix polynomial expansion tothe right one, the authors propose to accomplish a number of unimodal transformations of the matrix of the object’s "denominator", which will result in bringing unimodal matrices into different sections of a structure chart. In this case, equivalent transformations are performed. They "equalize" the column/row degrees of the polynomial matrix of the "denominator" of the object (in order to retain equivalence there are in-troduced at once two unimodal matrices, opposite to each other). The proposed technique is illus-trated by the example of a two-channel system corresponding to a dynamical system, which, in its turn is corresponding to a three-mass system with springs.