- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 695816, 7 pages
On Exponential Stability of Composite Stochastic Control Systems
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM, 43400 Serdang, Selangor, Malaysia
Received 28 November 2012; Revised 29 January 2013; Accepted 31 January 2013
Academic Editor: Ryan Loxton
Copyright © 2013 Fakhreddin Abedi and Wah June Leong. 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.
- R. Z. Khasminskii, Stochastic Stability of Differential Equations, vol. 7, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.
- J. Spiliotis and J. Tsinias, “Notions of exponential robust stochastic stability, ISS and their Lyapunov characterization,” International Journal of Robust and Nonlinear Control, vol. 13, no. 2, pp. 173–187, 2003.
- P. Florchinger, “Global stabilization of composite stochastic systems,” Computers & Mathematics with Applications, vol. 33, no. 6, pp. 127–135, 1997.
- C. Boulanger, “Stabilization of a class of nonlinear composite stochastic systems,” Stochastic Analysis and Applications, vol. 18, no. 5, pp. 723–735, 2000.
- R. L. Rusinek, “String stability of singularly perturbed stochastic systems,” Annales Mathematicae Silesianae, vol. 16, pp. 43–55, 2003.
- M. Krstic and H. Deng, Stabilization of Uncertain Nonlinear Systems, Springer, New York, NY, USA, 1998.
- J. Tsinias, “The concept of “exponential input to state stability” for stochastic systems and applications to feedback stabilization,” Systems & Control Letters, vol. 36, no. 3, pp. 221–229, 1999.
- H. Deng and M. Krstić, “Output-feedback stochastic nonlinear stabilization,” IEEE Transactions on Automatic Control, vol. 44, no. 2, pp. 328–333, 1999.
- T. Caraballo and K. Liu, “On exponential stability criteria of stochastic partial differential equations,” Stochastic Processes and Their Applications, vol. 83, no. 2, pp. 289–301, 1999.
- X. Mao, Exponential Stability of Stochastic Differential Equations, vol. 182, Marcel Dekker, New York, NY, USA, 1994.
- R. Liu and Y. Raffoul, “Boundedness and exponential stability of highly nonlinear stochastic differential equations,” Electronic Journal of Differential Equations, vol. 143, pp. 1–10, 2009.
- T. T. T. Lan and N. H. Dang, “Exponential stability of nontrivial solutions of stochastic differential equations,” Scientia A, vol. 21, pp. 97–106, 2011.
- J. Luo, “Exponential stability for stochastic neutral partial functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 355, no. 1, pp. 414–425, 2009.
- F. Abedi, M. A. Hassan, and N. M. Arifin, “Lyapunov function for nonuniform in time global asymptotic stability in probability with application to feedback stabilization,” Acta Applicandae Mathematicae, vol. 116, no. 1, pp. 107–117, 2011.
- F. Abedi and W. J. Leong, “Dynamic robust stabilization of stochastic differential control systems,” IMA Journal of Mathematical Control and Information, 2013.
- H. J. Kushner, “On the stability of processes defined by stochastic difference-differential equations,” Journal of Differential Equations, vol. 4, pp. 424–443, 1968.
- A. N. Michel, “Stability analysis of stochastic composite systems,” IEEE Transactions on Automatic Control, vol. AC-20, pp. 246–250, 1975.
- D. E. Sontag and Y. Wang, “On characterizations of input-to-state stability properties,” Systems and Control Letters, vol. 24, pp. 226–231, 1995.
- L. Arnold, Stochastic Differential Equations: Theory and Applications, John Wiley & Sons, New York, NY, USA, 1974.
- P. Florchinger, “A new decomposition method for stochastic dynamic stabilization,” Computers & Mathematics with Applications, vol. 29, no. 3, pp. 31–36, 1995.