Abstract
In Chap. 6 the general method of construction of Lyapunov functionals is used to get the asymptotic mean-square stability conditions for stochastic linear differential equations with constant delay, with distributed delay, and with variable bounded and unbounded delays. Sufficient stability conditions are formulated in terms of the existence of positive definite solutions of some matrix Riccati equations. Via the procedure of constructing Lyapunov functionals it is shown that for one stochastic linear differential equation, several different matrix Riccati equations can be obtained that allow one to get different stability conditions.
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Kolmanovskii VB, Nosov VR (1981) Stability and periodical regimes of regulating hereditary systems. Nauka, Moscow (in Russian)
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© 2013 Springer International Publishing Switzerland
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Shaikhet, L. (2013). Matrix Riccati Equations in Stability of Linear Stochastic Differential Equations with Delays. In: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00101-2_6
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DOI: https://doi.org/10.1007/978-3-319-00101-2_6
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00100-5
Online ISBN: 978-3-319-00101-2
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