On Integration of a Matrix Riccati Equation

Abstract

We execute the complete integration of the simplest matrix Riccati equation in the two- and three-dimensional cases for an arbitrary linear differential operator. The solution is constructed in terms of the Jordan form of an unknown matrix and the corresponding similarity matrix. We show that a similarity matrix is always representable as the product of two matrices one of which is an invariant of the differential operator.

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Funding

The authors were supported by the Programs of Basic Research nos. III.22.4.1 and I.1.5 (project no. 0314–2019–0011) of the Siberian Branch of the Russian Academy of Sciences.

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Correspondence to M. V. Neshchadim or A. P. Chupakhin.

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Translated by Ya.A.Kopylov

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Neshchadim, M.V., Chupakhin, A.P. On Integration of a Matrix Riccati Equation. J. Appl. Ind. Math. 14, 732–742 (2020). https://doi.org/10.1134/S1990478920040110

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Keywords

  • matrix Riccati equation
  • algebraic invariant
  • Jordan form