Relationship between canonical forms of linear differential observation systems and canonical forms of their discrete approximations

摘要

We establish a relationship between the canonical form of a linear differential system and the canonical form of its discrete approximation based on the replacement of the derivative by Euler's finite difference. We prove that if there exist limits of certain sequences of discrete functions constructed with the use of coefficients of the canonical form of the discrete system, then these limits define the canonical form of the differential system.