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In this paper, exponential stability of infinite dimensional stochastic systems with delay is considered. Firstly, we construct the suitable Lyapunov functions. And then sufficient conditions for exponential stability of infinite dimensional linear stochastic systems with delay are derived by using Itô formula and Poincaré inequality in partial differential equations. The conditions are formulated...
In this article, we discuss infinite linear stochastic systems with constants, varying-delays and multi-varying delays. Based on Lyapunov stability theory, by infinite dimensional Itô formula and linear operator inequality(LOI), several sufficient conditions for mean square exponential stability are derived. A example about stability of stochastic heat equation is given to illustrate the proposed...
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