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Mathematical Problems in Engineering
Volume 2015, Article ID 584935, 7 pages
Research Article

Lyapunov Characterization for the Stability of Stochastic Control Systems

1Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137 66731, Iran
3Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran 16589 53571, Iran

Received 20 May 2014; Accepted 21 August 2014

Academic Editor: Giuseppe Rega

Copyright © 2015 Fakhreddin Abedi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Lyapunov-like characterization for the problem of input-to-state stability in the probability of nonautonomous stochastic control systems is established. We extend the well-known Artstein-Sontag theorem to derive the necessary and sufficient conditions for the input-to-state stabilization of stochastic control systems. Illustrating example is provided.