Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 4, Pages 209-226

Analysis of stability problems via matrix Lyapunov functions

Anatoly A. Martynyuk

Institute of Mechanics, the Ukranian Academy of Sciences, Nesterov Str. 3, Kiev-57 252057, Russia

Received 1 April 1990; Revised 1 October 1990

Copyright © 1990 Anatoly A. Martynyuk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The stability of nonlinear systems is analyzed by the direct Lyapunov's method in terms of Lyapunov matrix functions. The given paper surveys the main theorems on stability, asymptotic stability and nonstability. They are applied to systems of nonlinear equations, singularly-perturbed systems and hybrid systems. The results are demonstrated by an example of a two-component system.