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Mat. Zametki, 2001, Volume 69, Issue 2, Pages 163–170 (Mi mz492)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalized Gram Matrix and Its Application to the Observability Problem for Linear Nonsteady Systems

A. I. Astrovskii

Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

Abstract: Sufficient conditions for the nondegeneracy of a generalized Gram matrix are obtained. In particular, it is shown that the generalized Gram matrix is nondegenerate for the Chebyshev systems of functions. An application of the results to the observability problems for linear nonsteady systems of ordinary differential equations are given. In terms of the observability matrix, necessary and sufficient conditions of the complete and total observability by means of finite-parameter solving operations are established.

DOI: https://doi.org/10.4213/mzm492

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English version:
Mathematical Notes, 2001, 69:2, 141–148

Bibliographic databases:

UDC: 517.977
Received: 26.12.1997

Citation: A. I. Astrovskii, “Generalized Gram Matrix and Its Application to the Observability Problem for Linear Nonsteady Systems”, Mat. Zametki, 69:2 (2001), 163–170; Math. Notes, 69:2 (2001), 141–148

Citation in format AMSBIB
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\pages 141--148
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Biryukov D.S., Ushakov A.V., “Gramiannyi podkhod k otsenke energeticheskikh zatrat na upravlenie v nepreryvnykh sistemakh pri statsionarnykh stokhasticheskikh vozdeistviyakh”, Izvestiya vysshikh uchebnykh zavedenii. Priborostroenie, 54:6 (2011), 36–42  elib
    2. Marchenko V.M., “Controllability and Observability of Hybrid Discrete-Continuous Systems in the Simplest Function Classes”, Differ. Equ., 51:11 (2015), 1461–1475  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Marchenko V.M., “On the complete controllability of hybrid differential-difference systems”, Differ. Equ., 52:12 (2016), 1624–1637  crossref  mathscinet  zmath  isi  scopus
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