Reduction of the Rosenbrock matrix in analysis of invariant zeros of the linear MIMO-System

The problem is considered of reduction of the Rosenbrock matrix in analysis of invariant zeros of a linear multidimensional dynamical system with many inputs and many outputs. Approaches to the Rosenbrock matrix reduction are compared, which are carried out with the aid of the transformation of initial system equations to the Yokoyama canonical form and on the basis of zero divisors of numerical matrices. It is shown that the approach to the Rosenbrock matrix reduction on the basis of zero divisors is less arduous and offers the possibility of obtaining a well-posed problem in eigenvalues of the generalized linear bundle, while the reduction on the basis of subspaces of A. N. Krylov leads to the problem in eigenvalues of the nonlinear (polynomial) bundle of matrices, and its stipulation is generally rather poor. Various versions of the reduced matrices are presented, which are obtained in accordance with properties of the dynamical system. Properties of the Rosenbrock reduced matrices are analyzed.