Nonlinear Phenomena in Complex Systems, 2007, Vol.10, No.3, pp.218-227

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2007, Vol.10, No.3, pp.218-227

Impulsive Matrix Differential Equations and Stability Properties of their Solutions.
V.A. Chiricalov

The main purpose of the paper is to consider applications of the second Lyapunov's method for investigation of the stability of trivial solution of matrix impulsive differential equation. Because the impulsive equation is connected with some difference equation, we consider direct Lyapunov's method for investigation of stability properties of difference equations. This allowed us to exchange the study of stability properties of differential equation by studying of stability properties of difference one. Some analog of Lyapunov's theorems for matrix difference equations have been considered. For linear matrix difference equations some Lyapunov's functions have been proposed. The idea of their construction based on the ideas of M.G.Krein.
Key words: impulsive matrix differential equation, matrix difference equation, second Lyapunov's method, stability conditions

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