Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gaishun, I.V., Vvedenie v teoriyu lineinykh nestatsionarnykh sistem (Introduction to Theory of Linear Nonstationary Systems), Moscow, 2004.
Astrovskii, A.I. and Gaishun, I.V., Quasidifferentiability and Observability of Linear Nonstationary Systems, Differ. Uravn., 2009, vol. 45, no. 11, pp. 1567–1576.
Astrovskii, A.I. and Gaishun, I.V., Quasidifferentiability and Canonical Forms of Linear Nonstationary Observation Systems, Differ. Uravn., 2010, vol. 46, no. 3, pp. 423–431.
Astrovskii, A.I. and Gaishun, I.V., One Way of Constructing Frobenius Canonical Forms of Linear Nonstationary Observation Systems, Differ. Uravn., 2010, vol. 46, no. 10, pp. 1479–1487.
Astrovskii, A.I. and Gaishun, I.V., Canonical Forms of Linear Nonstationary Observation Systems with Quasidifferentiable Coefficients under Various Transformation Groups, Differ. Uravn., 2011, vol. 47, no. 2, pp. 254–263.
Gaishun, I.V., Sistemy s diskretnym vremenem (Systems with Discrete Time), Minsk, 2001.
Derr, V.Ya., Nonoscillation of Solutions of a Linear Quasidifferential Equation, Izv. Inst. Mat. i Inform. Udmurt. Gos. Univ., Izhevsk, 1999, vol. 1(16), pp. 3–105.
Teptin, A.L., On Certain Properties of Solutions of Linear Difference Equations Approximating Differential Equations in the Interval of Nonoscillation, Differ. Uravn., 1965, vol. 1, no. 4, pp. 478–498.
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.I. Astrovskii, I.V. Gaishun, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 7, pp. 954–962.
Rights and permissions
About this article
Cite this article
Astrovskii, A.I., Gaishun, I.V. Relationship between canonical forms of linear differential observation systems and canonical forms of their discrete approximations. Diff Equat 47, 963–971 (2011). https://doi.org/10.1134/S0012266111070056
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266111070056