Geodesic
An application of the second Lyapunov method to stability investigation of differential equations with deviations
Archivum mathematicum, Tome 34 (1998) no. 1, pp. 127-142
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The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, as well as non-linear control systems and systems with quadratic and rational right hand sides.
The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, as well as non-linear control systems and systems with quadratic and rational right hand sides.
Classification : 34D20, 34K20, 34K35, 93D05
Keywords: Stability; Lyapunov functional; asymptotic stability 
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Khusainov, Denis. An application of the second Lyapunov method to stability investigation of differential equations with deviations. Archivum mathematicum, Tome 34 (1998) no. 1, pp. 127-142. http://geodesic.mathdoc.fr/item/ARM_1998_34_1_a12/

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