An application of the second Lyapunov method to stability investigation of differential equations with deviations. (English) Zbl 0915.34066

Khusainov, Denis

Arch. Math., Brno 34, No. 1, 127-142 (1998).

This interesting paper presents an overview of A. M. Lyapunov’s direct method to the stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskij functionals for linear systems with constant coefficients are considered. Quadratic functionals in a general form and Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, and nonlinear control systems and systems with quadratic and rational right-hand sides. The Razumikhin condition is supposed. Many connections with the author’s own results and an overview of author’s results are given, too.

Reviewer: J.Diblík (Brno)

MSC:

34K20	Stability theory of functional-differential equations
34D20	Stability of solutions to ordinary differential equations

Keywords:

stability; Lyapunov functional; asymptotic stability