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Systems of Linear Equations with Varying Delays

  • Leonid Shaikhet

Abstract

In this chapter the general method of the construction of Lyapunov functionals is used for constructing the asymptotic mean square stability conditions for stochastic linear difference equations with varying delays. Different ways of the construction of Lyapunov functionals are shown for difference equations with nonincreasing delays and difference equations with unbounded delays. The stability conditions obtained are formulated in terms of the existence of positive definite solutions of different matrix Riccati equations.

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

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

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