An Interdisciplinary Journal

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

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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Last updated: *October 8, 2007*