Abstract
New stochastic averaging theorems are presented that relax the key limiting conditions in the existing stochastic averaging theory. First a notion of weak stability under random perturbation is introduced for general nonlinear systems that violate the equilibrium condition for the original system. This stability notion is a stability robustness property for a deterministic system, relative to perturbations involving a stochastic process, and in the presence of a small parameter. Then stability-like properties are studied for the original system by investigating the weak stability under the random perturbation of the equilibrium of the average system.
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© 2012 Springer-Verlag London
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Liu, SJ., Krstic, M. (2012). Stochastic Averaging for Practical Stability. In: Stochastic Averaging and Stochastic Extremum Seeking. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4087-0_4
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DOI: https://doi.org/10.1007/978-1-4471-4087-0_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4086-3
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