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ASYMPTOTIC BEHAVIOURS OF STOCHASTIC DIFFERENTIAL DELAY EQUATIONS
Author(s) -
Shen Yi,
Mao Xuerong
Publication year - 2006
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2006.tb00247.x
Subject(s) - lyapunov function , mathematics , exponential stability , stochastic differential equation , lyapunov redesign , stability (learning theory) , lyapunov equation , control theory (sociology) , computer science , nonlinear system , control (management) , artificial intelligence , physics , quantum mechanics , machine learning
Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper. We shall establish the sufficient condition, in terms of multiple Lyapunov functions, for the asymptotic behaviours of solutions of stochastic differential delay equations. Moreover, from them follow many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in applications. In particular, the well‐known classical theorem on stochastic asymptotic stability is a special case of our more general results. These show clearly the power of our new results. Two examples are also given for illustration.