Stability criteria for systems of two first-order linear ordinary differential equations

Author:

Grigorian Gevorg A.1

Affiliation:

1. Institute of Mathematics NAS of Armenia M. Bagramian 24/5 Yerevan Armenia

Abstract

Abstract The Riccati equation method is used to establish stability criteria for systems of two first-order linear ordinary differential equations. Examples are presented in which the obtained result is 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference24 articles.

1. ADRIANOBA, L. Y.: Introduction to the Theory of Linear Systems of Differential Equations., Publishers of St. Petersburg University, S. Peterburg, 1992.

2. ASHORDIA, M.: Lyapunov Stability of systems of linear generalized ordinary differential equations, Comput. Math. Appl. 50 (2005), 957–982.

3. BELLMAN, R.; Stability Theory of Differential Equations, Foreign Literature Publishers, Moscow, 1954.

4. BELLMAN, R.: On an application of a Banach-Steinhaus theorem to the study of the boundedness of solutions of nonlinear differential and difference equations, Ann. Math. 49(2) (1948), 515–522.

5. BURDINA, V. I.: On boundedness of solutions of systems of differential equations, Dokl. AN SSSR 93(4) (1953), 603–606.

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