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.
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© 2011 Springer-Verlag London Limited
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Shaikhet, L. (2011). Systems of Linear Equations with Varying Delays. In: Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer, London. https://doi.org/10.1007/978-0-85729-685-6_6
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DOI: https://doi.org/10.1007/978-0-85729-685-6_6
Publisher Name: Springer, London
Print ISBN: 978-0-85729-684-9
Online ISBN: 978-0-85729-685-6
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