Approximation Approach to Construct Canonical Forms for Linear Time–Varying Observation Systems with Scalar Output

We establish a relationship between the canonical form of a linear differential system and the canonical form of its discrete approximation obtained by replacing the derivative with the Euler finite difference. We prove that if there exist limits of certain sequences of discrete functions constructed with coefficients of the canonical form of the discrete system, then these limits define the canonical form of the differential system. Some examples are given.