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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 263045, 9 pages
Finite-Time Stability and Stabilization of Itô-Type Stochastic Singular Systems
1School of Electrical Engineering and Automation, Qilu University of Technology, Jinan 250353, China
2College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China
Received 14 October 2013; Accepted 19 November 2013; Published 14 January 2014
Academic Editor: Hui Zhang
Copyright © 2014 Zhiguo Yan and Weihai Zhang. 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.
- X. Mao, Stochastic Differential Equations and Applications, Horwood Publishing, London, UK, 2nd edition, 2008.
- W. Zhang and B.-S. Chen, “-representation and applications to generalized Lyapunov equations and linear stochastic systems,” IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3009–3022, 2012.
- Z. Lin, J. Liu, W. Zhang, and Y. Niu, “Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach,” Automatica, vol. 47, no. 12, pp. 2796–2800, 2011.
- D. Hinrichsen and A. J. Pritchard, “Stochastic ,” SIAM Journal on Control and Optimization, vol. 36, no. 5, pp. 1504–1538, 1998.
- 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, “A unified design for state and output feedback control of nonlinear stochastic Markovian jump systems with state and disturbance-dependent noise,” Automatica, vol. 45, no. 12, pp. 2955–2962, 2009.
- 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.
- X.-J. Xie and N. Duan, “Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1197–1202, 2010.
- J. Y. Ishihara and M. H. Terra, “On the Lyapunov theorem for singular systems,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1926–1930, 2002.
- G. Zhang and W. Liu, “Impulsive mode elimination for descriptor systems by a structured P-D feedback,” IEEE Transactions on Automatic Control, vol. 56, no. 12, pp. 2968–2973, 2011.
- J. Zhu, S. Ma, and Z. Cheng, “Singular LQ problem for nonregular descriptor systems,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1128–1133, 2002.
- S. Xu, J. Lam, and Y. Zou, “ filtering for singular systems,” IEEE Transactions on Automatic Control, vol. 48, no. 12, pp. 2217–2222, 2003.
- L. Zhang, B. Huang, and J. Lam, “LMI synthesis of and mixed / controllers for singular systems,” IEEE Transactions on Circuits and Systems II, vol. 50, no. 9, pp. 615–626, 2003.
- Z. Yan, G. Zhang, and J. Wang, “Infinite horizon / control for descriptor systems: nash game approach,” Journal of Control Theory and Applications, vol. 10, no. 2, pp. 159–165, 2012.
- L. Huang and X. Mao, “Stability of singular stochastic systems with Markovian switching,” IEEE Transactions on Automatic Control, vol. 56, no. 2, pp. 424–429, 2011.
- J. Xia, Robust control and filter for continuous stochstic time-delay systems [Ph.D. dissertation], Nanjing University of Science and Technology, Nanjing, China, 2007.
- F. Amato, M. Ariola, and P. Dorato, “Finite-time control of linear systems subject to parametric uncertainties and disturbances,” Automatica, vol. 37, no. 9, pp. 1459–1463, 2001.
- F. Amato and M. Ariola, “Finite-time control of discrete-time linear systems,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 724–729, 2005.
- W. Zhang and X. An, “Finite-time control of linear stochastic systems,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 3, pp. 687–694, 2008.
- Z. Yan, G. Zhang, and J. Wang, “Non-fragile robust finite-time control for nonlinear stochastic Itô systems using neural network,” International Journal of Control, Automation and Systems, vol. 10, no. 5, pp. 873–882, 2012.
- Z. G. Yan and G. S. Zhang, “Finite-time control for linear stochastic systems,” Control and Decision, vol. 26, no. 8, pp. 1224–1228, 2011.
- Z. G. Yan and G. S. Zhang, “Finite-time filtering for a class of nonlinear stochastic uncertain systems,” Control and Decision, vol. 29, no. 3, pp. 419–424, 2012.
- J. Feng, Z. Wu, and J. Sun, “Finite-time control of linear singular systems with parametric uncertainties and disturbances,” Acta Automatica Sinica, vol. 31, no. 4, pp. 634–637, 2005.
- Y. Zhang, C. Liu, and X. Mu, “Robust finite-time control of singular stochastic systems via static output feedback,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5629–5640, 2012.
- S. Xing, Q. Zhang, and Y. Zhang, “Finite-time stability analysis and control for a class of stochastic singular biological economic systems based on T-S fuzzy model,” Abstract and Applied Analysis, vol. 2013, Article ID 946491, 10 pages, 2013.
- Z. Yan, G. Zhang, and W. Zhang, “Finite-time stability and stabilization of linear Itô stochastic systems with state and control-dependent noise,” Asian Journal of Control, vol. 15, no. 1, pp. 270–281, 2013.
- B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, New York, NY, USA, 5th edition, 2000.
- L. Dai, Singular Control Systems, Springer, Berlin, Germany, 1989.
- H. Zhang, J. Wang, and Y. Shi, “Robust sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities,” Systems & Control Letters, vol. 62, no. 12, pp. 1114–1124, 2013.
- H. Zhang, Y. Shi, and M. Liu, “ switched filtering for networked systems based on delay occurrence probabilities,” Journal of Dynamic Systems, Measurement, and Control, vol. 135, no. 6, Article ID 061002, 5 pages, 2013.
- H. Zhang, Y. Shi, and A. S. Mehr, “Parameter-dependent mixed filtering for linear parameter-varying systems,” IET Signal Processing, vol. 6, no. 7, pp. 697–703, 2012.