CONSTRUCTION OF THE TRANSITION MATRIX OF A DISCRETE CONTROL SYSTEM

Abstract

This article discusses a method for constructing a transition matrix for discrete control systems, a key step in solving difference equations. The authors propose using the Cayley-Hamilton theorem to efficiently calculate the matrix degree when discrete time assumes large values. The method is based on representing the transition matrix as a polynomial in a matrix of degree at most n-1, where the coefficients are determined through the system's eigenvalues.