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An application of the second Lyapunov method to stability investigation of differential equations with deviations

Denis Khusainov — 1998

Archivum Mathematicum

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...

Asymptotic estimation of the convergence of solutions of the equation x ˙ ( t ) = b ( t ) x ( t - τ ( t ) )

Josef Diblík;  Denis Khusainov — 2001

Archivum Mathematicum

The main result of the present paper is obtaining new inequalities for solutions of scalar equation x ˙ ( t ) = b ( t ) x ( t - τ ( t ) ) . Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution x ( t ) reaches an ε - neighbourhood of origin and remains in it.

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