- 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
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 867189, 7 pages
Finite Time Stability of Stochastic Hybrid Systems
Department of Mathematics, Huizhou University, Huizhou 516007, China
Received 20 October 2013; Accepted 20 December 2013; Published 16 January 2014
Academic Editor: Ademir Fernando Pazoto
Copyright © 2014 Ying Yang and Guopei Chen. 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.
- H. I. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer, New York, NY, USA, 2001.
- J. P. Hespanha, “A model for stochastic hybrid systems with application to communication networks,” Nonlinear Analysis: Theory, Methods and Applications, vol. 62, no. 8, pp. 1353–1383, 2005.
- Y. Ji and H. J. Chizeck, “Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control,” IEEE Transactions on Automatic Control, vol. 35, no. 7, pp. 777–788, 1990.
- X. Mao and C. Yuan, “Asymptotic stability in distribution of stochastic differential equations with Markovian switching,” Stochastic Processes and Their Applications, vol. 103, no. 2, pp. 277–291, 2003.
- L. Hu, P. Shi, and B. Huang, “Stochastic stability and robust control for sampled-data systems with Markovian jump parameters,” Journal of Mathematical Analysis and Applications, vol. 313, no. 2, pp. 504–517, 2006.
- V. Dragan and T. Morozan, “Stability and robust stabilization to linear stochastic systems described by differential equations with Markovian jumping and multiplicative white noise,” Stochastic Analysis and Applications, vol. 20, no. 1, pp. 33–92, 2002.
- S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000.
- E. Moulay and W. Perruquetti, “Finite time stability and stabilization of a class of continuous systems,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1430–1443, 2006.
- E. Moulay and W. Perruquetti, “Finite time stability conditions for non-autonomous continuous systems,” International Journal of Control, vol. 81, no. 5, pp. 797–803, 2008.
- E. Moulay, M. Dambrine, N. Yeganefar, and W. Perruquetti, “Finite-time stability and stabilization of time-delay systems,” Systems and Control Letters, vol. 57, no. 7, pp. 561–566, 2008.
- Y. Hong, Z.-P. Jiang, and G. Feng, “Finite-time input-to-state stability and applications to finite-time control design,” SIAM Journal on Control and Optimization, vol. 48, no. 7, pp. 4395–4418, 2010.
- Y. Hong, J. Huang, and Y. Xu, “On an output feedback finite-time stabilization problem,” IEEE Transactions on Automatic Control, vol. 46, no. 2, pp. 305–309, 2001.
- Y. Hong, J. Wang, and D. Cheng, “Adaptive finite-time control of nonlinear systems with parametric uncertainty,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 858–862, 2006.
- X. Huang, W. Lin, and B. Yang, “Global finite-time stabilization of a class of uncertain nonlinear systems,” Automatica, vol. 41, no. 5, pp. 881–888, 2005.
- Z.-P. Jiang and I. M. Y. Mareels, “A small-gain control method for nonlinear cascaded systems with dynamic uncertainties,” IEEE Transactions on Automatic Control, vol. 42, no. 3, pp. 292–308, 1997.
- Y. Wu, X. Yu, and Z. Man, “Terminal sliding mode control design for uncertain dynamic systems,” Systems and Control Letters, vol. 34, no. 5, pp. 281–287, 1998.
- X. Yu and M. Zhihong, “Fast terminal sliding-mode control design for nonlinear dynamical systems,” IEEE Transactions on Circuits and Systems I, vol. 49, no. 2, pp. 261–264, 2002.
- S. Yu, X. Yu, B. Shirinzadeh, and Z. Man, “Continuous finite-time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957–1964, 2005.
- W. Chen and L. C. Jiao, “Finite-time stability theorem of stochastic nonlinear systems,” Automatica, vol. 46, no. 12, pp. 2105–2108, 2010.
- J. Yin, S. Khoo, Z. Man, and X. Yu, “Finite-time stability and instability of stochastic nonlinear systems,” Automatica, vol. 47, no. 12, pp. 2671–2677, 2011.
- R. Situ, Theory of Stochastic Differential Equations with Jumps and Appli-Cations: Mathematical and Analysis Techniques with Applications to Engineering, Springer, New York, NY, USA, 2005.
- A. V. Skorohod, Symptotic Methods in the Theory of Stochastic Differential Equations, American Mathematical Society, Providence, RI, USA, 2004.