Journal of Applied Mathematics and Stochastic Analysis 
Volume 3 (1990), Issue 4, Pages 209-226
doi:10.1155/S104895339000020X

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

Abstract

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.