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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 747890, 8 pages
Robust Filter Design for Itô Stochastic Pantograph Systems
1School of Electrical Engineering and Automation, Shandong Polytechnic University, Jinan 250353, China
2School of Science, Shandong Polytechnic University, Jinan 250353, China
Received 20 January 2013; Accepted 18 February 2013
Academic Editor: Weihai Zhang
Copyright © 2013 Zhiguo Yan and Yulin Huang. 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.
- C. T. H. Baker and E. Buckwar, “Continuous -methods for the stochastic pantograph equation,” Electronic Transactions on Numerical Analysis, vol. 11, pp. 131–151, 2000.
- J. A. Appleby and E. Buckwar, “Sufficient condition for polynomial asymptotic behavior of the stochastic pantograph equation,” http://www4.dcu.ie/maths/research/preprint.shtml.
- Z. Fan, M. Song, and M. Liu, “The -th moment stability for the stochastic pantograph equation,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 109–120, 2009.
- L. Ronghua, L. Min, and P. Wan-kai, “Convergence of numerical solutions to stochastic pantograph equations with Markovian switching,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 414–422, 2009.
- F. Jiang, H. Yang, and S. Wang, “Asymptotic stability of stochastic pantograph differential equations with Markovian switching,” Journal of Nonlinear Analysis and Optimization, vol. 1, no. 1, pp. 9–16, 2010.
- B.-S. Chen and W. Zhang, “Stochastic control with state-dependent noise,” IEEE Transactions on Automatic Control, vol. 49, no. 1, pp. 45–57, 2004.
- W. Zhang and B.-S. Chen, “State feedback control for a class of nonlinear stochastic systems,” SIAM Journal on Control and Optimization, vol. 44, no. 6, pp. 1973–1991, 2006.
- Z. Lin, Y. Lin, and W. Zhang, “ filtering for non-linear stochastic Markovian jump systems,” IET Control Theory & Applications, vol. 4, no. 12, pp. 2743–2756, 2010.
- X. Guo, G. Yang, and W. Che, “Insensitive dynamic output feedback control with mixed- norm sensitivity minimization,” Journal of the Franklin Institute, vol. 350, no. 1, pp. 72–91, 2013.
- E. Gershon, D. J. N. Limebeer, U. Shaked, and I. Yaesh, “Robust filtering of stationary continuous-time linear systems with stochastic uncertainties,” IEEE Transactions on Automatic Control, vol. 46, no. 11, pp. 1788–1793, 2001.
- S. Xu and T. Chen, “Reduced-order filtering for stochastic systems,” IEEE Transactions on Signal Processing, vol. 50, no. 12, pp. 2998–3007, 2002.
- W. Zhang, B.-S. Chen, and C.-S. Tseng, “Robust filtering for nonlinear stochastic systems,” IEEE Transactions on Signal Processing, vol. 53, no. 2, pp. 589–598, 2005.
- W. Zhang, B. S. Chen, L. Sheng, and M. Gao, “Robust / filter design for a class of nonlinear stochastic systems with state-dependent noise,” Mathematical Problems in Engineering, vol. 2012, Article ID 750841, 16 pages, 2012.
- Z. G. Yan and G. S. Zhang, “Finite-time filtering for a class of nonlinear stochastic uncertain systems,” Control and Decision, vol. 27, no. 3, pp. 419–424, 2012.
- R. Z. Hasminskii, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.