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Linear Equations with Stationary Coefficients

  • Leonid Shaikhet

Abstract

Here the procedure of Lyapunov functionals construction described in Chap.  1 is applied to the difference equation with stationary coefficients in a general form. Four different ways of Lyapunov functionals construction are shown that allows to get four different types of sufficient conditions for asymptotic mean square stability of the trivial solution of the considered equation. One generalization of obtained stability conditions are shown also. Besides the special investigation of asymptotic behavior of the solution of difference equation via characteristic equation are shown. The results of investigations are illustrated by figures with obtained stability regions and trajectories of solutions.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Higher MathematicsDonetsk State University of ManagementDonetskUkraine

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