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Stability of stochastic differential equations with additive persistent noise
D. Mateos-Nunez, J. Cortés
Proceedings of the American Control Conference, Washington, D.C., USA, 2013, pp. 5447-5452

Abstract

We present a stability result for stochastic differential equations subject to additive persistent noise. Specifically, we propose a Lyapunov test for noise-to-state stability in $p$th~moment with respect to an arbitrary subspace. To check the hypotheses of our result, we develop a method that exploits equivalence relations between seminorms and a family of positive semidefinite functions. With this method, we can translate inequalities between two positive semidefinite functions into separate sets of geometric conditions that relate each of them to a seminorm.

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