- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 560647, 10 pages
On the Asymptotical and Practical Stability of Stochastic Control Systems
Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
Received 24 October 2012; Accepted 18 January 2013
Academic Editor: Vu Phat
Copyright © 2013 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.
- I. Karafyllis and J. Tsinias, “A converse Lyapunov theorem for nonuniform in time global asymptotic stability and its application to feedback stabilization,” SIAM Journal on Control and Optimization, vol. 42, no. 3, pp. 936–965, 2003.
- V. N. Phat, Q. P. Ha, and H. Trinh, “Parameter-dependent control for time-varying delay polytopic systems,” Journal of Optimization Theory and Applications, vol. 147, no. 1, pp. 58–70, 2010.
- M. V. Thuan, V. N. Phat, and H. M. Trinh, “Dynamic output feedback guaranteed cost control for linear systems with interval time-varying delays in states and outputs,” Applied Mathematics and Computation, vol. 218, no. 21, pp. 10697–10707, 2012.
- N. S. Bay, N. M. Linh, and V. N. Phat, “Robust control of linear time-varying systems with mixed delays in the Hilbert space,” Optimal Control Applications & Methods, vol. 32, no. 5, pp. 545–557, 2011.
- H. Trinh and T. Fernando, Functional Observers for Dynamical Systems, vol. 420 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 2012.
- P. Florchinger, “Lyapunov-like techniques for stochastic stability,” SIAM Journal on Control and Optimization, vol. 33, no. 4, pp. 1151–1169, 1995.
- H. Deng and M. Krstić, “Stochastic nonlinear stabilization. I. A backstepping design,” Systems & Control Letters, vol. 32, no. 3, pp. 143–150, 1997.
- H. Deng, M. Krstić, and R. J. Williams, “Stabilization of stochastic nonlinear systems driven by noise of unknown covariance,” IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1237–1253, 2001.
- X.-J. Xie and J. Tian, “State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics,” International Journal of Robust and Nonlinear Control, vol. 17, no. 14, pp. 1343–1362, 2007.
- Z. Pan and T. Başar, “Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion,” SIAM Journal on Control and Optimization, vol. 37, no. 3, pp. 957–995, 1999.
- Z. Lin, J. Liu, Y. Lin, and W. Zhang, “Nonlinear stochastic passivity, feedback equivalence and global stabilization,” International Journal of Robust and Nonlinear Control, vol. 22, no. 9, pp. 999–1018, 2012.
- 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, M. A. Hassan, and M. Suleiman, “Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function,” Stochastics, vol. 83, no. 2, pp. 179–201, 2011.
- J. Tsinias, “Existence of control Lyapunov functions and applications to state feedback stabilizability of nonlinear systems,” SIAM Journal on Control and Optimization, vol. 29, no. 2, pp. 457–473, 1991.
- H. Kushner, “Converse theorems for stochastic Liapunov functions,” SIAM Journal on Control and Optimization, vol. 5, pp. 228–233, 1967.
- J. L. Speyer and W. H. Chung, Stochastic Processes, Estimation, and Control, vol. 17 of Advances in Design and Control, SIAM, Philadelphia, Pa, USA, 2008.
- R. Z. Has'minskiĭ, Stochastic Stability of Differential Equations, vol. 7 of Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.
- P. J. La Salle and S. Lefschetz, Stability by Liapunov's Direcct Method with Applications, Academic Press, New York, NY, USA, 1961.
- Z. Artstein, “Stabilization with relaxed controls,” Nonlinear Analysis: Theory, Methods & Applications, vol. 7, no. 11, pp. 1163–1173, 1983.
- P. Florchinger, “A stochastic Jurdjevic-Quinn theorem for the stabilization of nonlinear stochastic differential systems,” Stochastic Analysis and Applications, vol. 19, no. 3, pp. 473–480, 2001.
- J. L. Massera, “Contributions to stability theory,” Annals of Mathematics, vol. 64, pp. 182–206, 1956.
- J. L. Massera, “Erratum in “Contributions to stability theory”,” Annals of Mathematics, vol. 68, no. 1, p. 202, 1958.