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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 573439, 11 pages
pth Mean Practical Stability for Large-Scale Itô Stochastic Systems with Markovian Switching
1Department of Applied Mathematics, Donghua University, Shanghai 201620, China
2Department of Electronics and Information Engineering, Putian University, Fujian Putian 351100, China
3College of Information Sciences and Technology, Donghua University, Shanghai 201620, China
Received 29 June 2011; Accepted 6 September 2011
Academic Editor: Zidong Wang
Copyright © 2012 Yan Yun 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.
- J. P. LaSalle and S. Lefschetz, Stability Theory by Liapunovs Direct Method with Applications, Academic Press, New York, NY, USA, 1961.
- A. A. Martynyuk, Practical Stability of Motion, Naukav a Dumka, Kiev, Ukraine, 1983.
- A. A. Martynyuk, “Averaging method in the theory of motion stability,” Nonlinear Vibration Problems, vol. 14, pp. 71–79, 1973.
- V. Laksmikantham, S. Leela, and A. A. Martynyuk, Practical Stability of Nonlinear Systems, World Scientific, Singapore, 1990.
- Z. S. Feng, Y. Q. Liu, and F. W. Guo, “Criteria for practical stability in the p-th mean of nonlinear stochastic systems,” Applied Mathematics and Computation, vol. 49, no. 2-3, pp. 251–260, 1992.
- A. H. Tsoi and B. Zhang, “Practical stabilities of Itô type nonlinear stochastic differential systems and related control problems,” Dynamic Systems and Applications, vol. 6, no. 1, pp. 107–124, 1997.
- G. S. Ladde and B. A. Lawrence, “Stability and convergence of large scale stochastic approximation procedures,” International Journal of Systems Science, vol. 26, no. 3, pp. 595–618, 1995.
- L. Shaikhet, “Stability of stochastic differential systems with Markovian Switching,” Stochastic Processes, vol. 2, no. 18, pp. 180–184, 1996.
- S. Sathananthan, Practical Stability Criteria for Nonlinear Ito-Type Stochastic Control Systems, Academic Press, New York, NY, USA, 2000.
- M. A. O. Xuerong, A. Matasov, and A. B. Piunovskiy, “Stochastic differential delay equations with Markovian switching,” Bernoulli, vol. 6, no. 1, pp. 73–90, 2000.
- P. Zhao, “Practical stability, controllability and optimal control of stochastic Markovian jump systems with time-delays,” Automatica, vol. 44, no. 12, pp. 3120–3125, 2008.
- X. Mao, “Robustness of stability of stochastic differential delay equations with Markovian Switching,” Stability and Control: Theory and Applications, vol. 3, no. 1, pp. 48–61, 2000.
- H. Gilsing, “On the stability of the Euler scheme for an affine stochastic delay differential equation with the delay,” Tech. Rep. 20,SFB 373, Humboldt University, Berlin, Germany, 2001.
- A. V. Swishchuk and Y. I. Kazmerchuk, “Stability of stochastic of differential delay Ito's equations with Possion Jumps and with Markovian Switching. Application to Financial Models,” Teoriya Veroyatnostei i Matematicheskaya Statistika, vol. 63 (63), 2001.
- J. Luo, J. Zou, and Z. Hou, “Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching,” Science in China. Series A, vol. 46, no. 1, pp. 129–138, 2003.
- D. D. Šiljak, Large-Scale Dynamic Systems: Stability and Structure, vol. 3 of North-Holland Series in System Science and Engineering, North-Holland, New York, NY, USA, 1979.
- S. Sathananthan and S. Suthaharan, “Practical stability criteria for large-scale nonlinear stochastic systems by decomposition and aggregation,” Dynamics of Continuous, Discrete & Impulsive Systems. Series A, vol. 8, no. 2, pp. 227–248, 2001.
- G. S. Ladde and V. Lakshmikantham, Random Differential Inequalities, vol. 150 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1980.
- H. Dong, Z. Wang, D. W.C. Ho, and H. Gao, “Robust H∞ filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: the finite-horizon case,” IEEE Transactions on Signal Processing, vol. 59, no. 7, pp. 3048–3057, 2011.
- Y. Tang, Z. Wang, W. K. Wong, J. Kurths, and J. Fang, “Multiobjective synchronization of coupled systems,” Chaos, vol. 21, no. 2, Article ID 025114, 2011.
- Z. Wang, J. Lam, L. Ma, Y. Bo, and Z. Guo, “Variance-constrained dissipative observer-based control for a class of nonlinear stochastic systems with degraded measurements,” Journal of Mathematical Analysis and Applications, vol. 377, no. 2, pp. 645–658, 2011.
- B. Shen, Z. Wang, Y. S. Hung, and G. Chesi, “Distributed H∞ filtering for polynomial nonlinear stochastic systems in sensor networks,” IEEE Transactions on Industrial Electronics, vol. 58, no. 5, pp. 1971–1979, 2011.
- J. Liang, Z. Wang, and X. Liu, “Distributed state estimation for discrete-time sensor networks with randomly varying nonlinearities and missing measurements,” IEEE Transactions on Neural Networks, vol. 22, no. 3, pp. 486–496, 2011.
- X. He, Z. Wang, Y. D. Ji, and D. H. Zhou, “Robust fault detection for networked systems with distributed sensors,” IEEE Transactions on Aerospace and Electronic Systems, vol. 47, no. 1, pp. 166–177, 2011.
- B. Shen, Z. Wang, and X. Liu, “Bounded H∞ synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon,” IEEE Transactions on Neural Networks, vol. 22, no. 1, pp. 145–157, 2011.
- B. Shen, Z. Wang, H. Shu, and G. Wei, “H∞ filtering for uncertain time-varying systems with multiple randomly occurred nonlinearities and successive packet dropouts,” International Journal of Robust and Nonlinear Control, vol. 21, no. 14, pp. 1693–1709, 2011.
- Z. Wang, D. W. C. Ho, H. Dong, and H. Gao, “Robust H∞ finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1716–1722, 2010.
- Z. Wang, Y. Liu, and X. Liu, “Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1656–1662, 2010.