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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 378376, 8 pages
Finite-Time Synchronization of Singular Hybrid Coupled Networks
1Research Center for Complex Systems and Network Sciences, and Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Received 20 December 2012; Accepted 11 February 2013
Academic Editor: Jong Hae Kim
Copyright © 2013 Cong Zheng and Jinde Cao. 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.
- F. L. Lewis, “A survey of linear singular systems,” Circuits, Systems, and Signal Processing, vol. 5, no. 1, pp. 3–36, 1986.
- S. Xu, P. Van Dooren, R. Ştefan, and J. Lam, “Robust stability and stabilization for singular systems with state delay and parameter uncertainty,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1122–1128, 2002.
- G. Lu and D. W. C. Ho, “Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 818–823, 2006.
- G. Grammel, “Robustness of exponential stability to singular perturbations and delays,” Systems & Control Letters, vol. 57, no. 6, pp. 505–510, 2008.
- D. M. Stipanović and D. D. Šiljak, “Robust stability and stabilization of discrete-time non-linear systems: the LMI approach,” International Journal of Control, vol. 74, no. 9, pp. 873–879, 2001.
- E. Uezato and M. Ikeda, “Strict LMI conditions for stability, robust stabilization, and control of descriptor systems,” in Proceedings of the 38th IEEE Conference on Decision and Control, pp. 4092–4097, Phoenix, Ariz, USA, 1999.
- P. Wang and J. Zhang, “Stability of solutions for nonlinear singular systems with delay,” Applied Mathematics Letters, vol. 25, no. 10, pp. 1291–1295, 2012.
- Y. Zhang, C. Liu, and X. Mu, “Robust finite-time stabilization of uncertain singular Markovian jump systems,” Applied Mathematical Modelling, vol. 36, no. 10, pp. 5109–5121, 2012.
- L. Q. Zhang, B. Huang, and J. Lam, “LMI synthesis of and mixed controllers for singular systems,” IEEE Transactions on Circuits and Systems II, vol. 50, pp. 615–626, 2003.
- I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, “ control for descriptor systems: a matrix inequalities approach,” Automatica, vol. 33, no. 4, pp. 669–673, 1997.
- S. Xu and J. Lam, Robust Control and Filtering of Singular Systems, vol. 332 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 2006.
- E. Fridman, “-control of linear state-delay descriptor systems: an LMI approach,” Linear Algebra and Its Applications, vol. 15, pp. 271–302, 2002.
- Y. Xia, J. Zhang, and E.-K. Boukas, “Control of discrete singular hybrid systems,” Automatica, vol. 44, no. 10, pp. 2635–2641, 2008.
- S. Xu and C. Yang, “ state feedback control for discrete singular systems,” IEEE Transactions on Automatic Control, vol. 45, no. 7, pp. 1405–1409, 2000.
- M. S. Mahmoud and N. B. Almutairi, “Stability and implementable filters for singular systems with nonlinear perturbations,” Nonlinear Dynamics, vol. 57, no. 3, pp. 401–410, 2009.
- Z. G. Feng and J. Lam, “Robust reliable dissipative filtering for discrete delay singular systems,” Signal Processing, vol. 92, pp. 3010–3025, 2012.
- W. J. Xiong, D. W. C. Ho, and J. D. Cao, “Synchronization analysis of singular hybrid coupled networks,” Physics Letters A, vol. 372, pp. 6633–6637, 2008.
- J. F. Zeng and J. D. Cao, “Synchronisation in singgular hybrid complex networks with delayed coupling,” International Journal of Systems, Control and Communications, vol. 3, pp. 144–157, 2011.
- J. H. Koo, D. H. Ji, and S. C. Won, “Synchronization of singular complex dynamical networks with time-varying delays,” Applied Mathematics and Computation, vol. 217, no. 8, pp. 3916–3923, 2010.
- H. J. Li, Z. J. Ning, Y. H. Yin, and Y. Tang, “Synchronization and state estimation for singular complex dynamical networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, pp. 194–208, 2013.
- S. Li, W. Tang, and J. Zhang, “Robust control for synchronization of singular complex delayed networks with stochastic switched coupling,” International Journal of Computer Mathematics, vol. 89, no. 10, pp. 1332–1344, 2012.
- J. Xu and J. Sun, “Finite-time stability of linear time-varying singular impulsive systems,” IET Control Theory & Applications, vol. 4, no. 10, pp. 2239–2244, 2010.
- 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.
- L. Wang, S. Sun, and C. Xia, “Finite-time stability of multi-agent system in disturbed environment,” Nonlinear Dynamics, vol. 67, no. 3, pp. 2009–2016, 2012.
- V. T. Haimo, “Finite time controllers,” SIAM Journal on Control and Optimization, vol. 24, no. 4, pp. 760–770, 1986.
- 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.
- Y. Chen and J. H. Lü, “Finite time synchronization of complex dynamical networks,” Journal of Systems Science and Mathematical Sciences, vol. 29, no. 10, pp. 1419–1430, 2009.
- H. Wang, Z. Han, Q. Xie, and W. Zhang, “Finite-time chaos control of unified chaotic systems with uncertain parameters,” Nonlinear Dynamics, vol. 55, no. 4, pp. 323–328, 2009.
- Y. Z. Sun, W. Li, and D. H. Zhao, “Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies,” Chaos, vol. 22, no. 2, Article ID 023152, 2012.
- N. Cai, W. Li, and Y. Jing, “Finite-time generalized synchronization of chaotic systems with different order,” Nonlinear Dynamics, vol. 64, no. 4, pp. 385–393, 2011.
- X. Yang and J. Cao, “Finite-time stochastic synchronization of complex networks,” Applied Mathematical Modelling, vol. 34, no. 11, pp. 3631–3641, 2010.
- S. Li and Y.-P. Tian, “Finite time synchronization of chaotic systems,” Chaos, Solitons and Fractals, vol. 15, no. 2, pp. 303–310, 2003.
- W. L. Yang, X. D. Xia, Y. C. Dong, and S. W. Zheng, “Finite time synchronization between two different chaotic systems with uncertain parameters,” Computer & Information Science, vol. 3, pp. 174–179, 2010.
- L. Wang and F. Xiao, “Finite-time consensus problems for networks of dynamic agents,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 950–955, 2010.
- S. Yang, J. Cao, and J. Lu, “A new protocol for finite-time consensus of detail-balanced multi-agent networks,” Chaos, vol. 22, Article ID 043134, 2012.
- L. Wang, Z. Chen, Z. Liu, and Z. Yuan, “Finite time agreement protocol design of multi-agent systems with communication delays,” Asian Journal of Control, vol. 11, no. 3, pp. 281–286, 2009.
- Q. Hui, W. M. Haddad, and S. P. Bhat, “Finite-time semistability and consensus for nonlinear dynamical networks,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1887–1900, 2008.
- Y. Shen and X. Xia, “Semi-global finite-time observers for nonlinear systems,” Automatica, vol. 44, no. 12, pp. 3152–3156, 2008.