Construction of Transforms of Specified Solutions of a Linear System with Respect to the Minimal Polynomials of State Space Vectors

Abstract

Linear stationary systems specified by equations of state are investigated. The objective is to construct Laplace transforms of the proper motion of the system and its responses by means of minimal polynomials of state space vectors, as well as columns and rows of matrices of the distribution of system inputs and outputs. These minimal polynomials constitute the basic constructive element of the description of the transforms of processes in the system. The proposed approach elaborates the method of A. N. Krylov and formalizes it in contemporary terms.