Journal
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
Volume 13, Issue 2, Pages 173-187Publisher
JOHN WILEY & SONS LTD
DOI: 10.1002/rnc.724
Keywords
robust stochastic stability; ISS; Lyapunov functions
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Concepts of exponential global robust stability for stochastic control systems are analysed in terms of Lyapunov functions. The main result of the paper constitutes a generalization of a converse stability theorem due to Khasminskii for stochastic differential equations and establishes that, under certain hypotheses, the origin is robustly exponentially stable in the rth mean, if and only if the system admits a Lyapunov function which is smooth except possibly at the origin. The main result concerning robust asymptotic stability enable us to derive a Lyapunov-like characterization for the concept of stochastic input-to-state stability (ISS). Copyright (C) 2003 John Wiley Sons, Ltd.
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