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On the stability of systems of two first-order linear ordinary differential equations

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Abstract

We use the Riccati equation method to establish necessary and sufficient stability conditions and a stability criterion for a system of two first-order linear ordinary differential equations. We present examples in which these results are compared with the results obtained by the Lyapunov and Bogdanov methods, by a method involving estimates of solutions in the Lozinskii logarithmic norms, and by the freezing method.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences, Erevan, Armenia

    G. A. Grigoryan

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  1. G. A. Grigoryan
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Correspondence to G. A. Grigoryan.

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Original Russian Text © G.A. Grigoryan, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 3, pp. 283–292.

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Grigoryan, G.A. On the stability of systems of two first-order linear ordinary differential equations. Diff Equat 51, 283–292 (2015). https://doi.org/10.1134/S0012266115030015

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  • DOI: https://doi.org/10.1134/S0012266115030015

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