Application of the Second Lyapunov Method to Stability Investigation of Differential Equations with Deviations

Denis Khusainov

Address. Faculty of Cybernetics, Kiev Taras Shevchenko University, 64 Vladimirskaya str., Kiev, 252033, Ukraine


Abstract. 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.

AMS classification. 34K20

Key words. Stability, Lyapunov functional, asymptotic stability