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Mat. Sb., 1991, Volume 182, Number 7, Pages 970–984 (Mi msb1336)  

This article is cited in 4 scientific papers (total in 4 papers)

On the theory of the matrix Riccati equation

M. I. Zelikin


Abstract: Various approaches to the study of the matrix Riccati equation with variable coefficients are investigated. It is proved that the complexification of such an equation determines a flow on the Seigel generalized upper half-plane and on each of the strata forming its boundary. The concept of the matrix cross-ratio of a quadruple of points of the Grassmann manifold $G_n(\mathbf R^{2n})$ is introduced, and applications of it are given. In particular, a criterion is given for the preservation of the isoclinic property for a pair of planes that are displaced by the flow on $G_n(\mathbf R^{2n})$ determined by a matrix Riccati equation with variable coefficients. Bilinear optimal control problems with a quadratic quality criterion are considered. The corresponding extremals are found along with the matrix Riccati equations determined by them.

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English version:
Mathematics of the USSR-Sbornik, 1992, 73:2, 341–354

Bibliographic databases:

UDC: 517.977
MSC: Primary 34G20; Secondary 15A22
Received: 11.07.1990

Citation: M. I. Zelikin, “On the theory of the matrix Riccati equation”, Mat. Sb., 182:7 (1991), 970–984; Math. USSR-Sb., 73:2 (1992), 341–354

Citation in format AMSBIB
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\by M.~I.~Zelikin
\paper On the theory of the matrix Riccati equation
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 7
\pages 970--984
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1128254}
\zmath{https://zbmath.org/?q=an:0774.49003|0747.49006}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..73..341Z}
\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 73
\issue 2
\pages 341--354
\crossref{https://doi.org/10.1070/SM1992v073n02ABEH002549}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992KF43400003}


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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. M. I. Zelikin, “On the theory of the matrix Riccati equation. II”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 213–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Zelikin M., “Quadratic System of Partial Differential Equation and Problems of Minimization of Multiple Integrals”, Dokl. Akad. Nauk, 358:1 (1998), 7–9  mathnet  mathscinet  zmath  isi
    3. G. Freiling, G. Jank, A. Sarychev, “Non — Blow — Up Conditions for Riccati — type Matrix Differential and Difference Equations”, Results. Math, 37:1-2 (2000), 84  crossref
    4. O. V. Aleksandrova, O. S. Gromasheva, G. Yu. Kosolapkin, “Metod pogruzheniya dlya resheniya zadachi Shturma — Liuvillya v matrichnoi postanovke”, Dalnevost. matem. zhurn., 12:2 (2012), 136–145  mathnet
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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