Existance theroms for the matrix Riccati equation <mml:math alttext="$W' + W P(t)W + Q(t) =  0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>W</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mi>W</mml:mi><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>W</mml:mi><mml:mo>+</mml:mo><mml:mi>Q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>

Jones, Robert A.

doi:https://doi.org/10.1155/S0161171278000022

International Journal of Mathematics and Mathematical Sciences

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Volume 1 | Article ID 218294 | https://doi.org/10.1155/S0161171278000022

Existance theroms for the matrix Riccati equation W′+WP(t)W+Q(t)=0

Robert A. Jones¹

Received18 Mar 1977

Revised27 Sept 1977

Abstract

Sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval. The criteria involve integral conditions on the coefficient matrices of the Riccati equation. The present results are compared with previously known results.

Copyright

Copyright © 1978 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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