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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 713847, 8 pages
On Boundedness and Attractiveness of Nonlinear Switched Delay Systems
1Department of Mathematics, China University of Petroleum (Beijing), Beijing 102249, China
2School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
3Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia
4School of Mathematical Science, Capital Normal University, Beijing 1000484, China
Received 1 August 2013; Accepted 29 October 2013
Academic Editor: Yong Hong Wu
Copyright © 2013 Yi Zhang 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.
- M. S. Branicky, Studies in hybrid systems: modeling, analysis, control [ScD Thesis], MIT EECS, 1995.
- Z. Li, Y. Soh, and C. Wen, Switched and Impulsive Systems, vol. 313 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 2005.
- D. Liberzon, Switching in Systems and Control, Systems & Control: Foundations & Applications, Birkhäuser, Boston, Mass, USA, 2003.
- W. P. Dayawansa and C. F. Martin, “A converse Lyapunov theorem for a class of dynamical systems which undergo switching,” IEEE Transactions on Automatic Control, vol. 44, no. 4, pp. 751–760, 1999.
- M. A. Wick, P. Peleties, and R. A. Decarlo, “Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems,” European Journal of Control, vol. 4, pp. 140–147, 1998.
- R. N. Shorten and K. S. Naredra, “On the stability and existence of common Lyapunov functions for stable linear switching systems,” in Proceedings of the IEEE Conference on Decision and Control, vol. 4, pp. 3723–3724, 1998.
- D. Liberzon, J. P. Hespanha, and A. S. Morse, “Stability of switched systems: a Lie-algebraic condition,” Systems & Control Letters, vol. 37, no. 3, pp. 117–122, 1999.
- H. Xu and K. L. Teo, “Exponential stability with -gain condition of nonlinear impulsive switched systems,” Institute of Electrical and Electronics Engineers, vol. 55, no. 10, pp. 2429–2433, 2010.
- J. Liu, X. Liu, and W.-C. Xie, “Generalized invariance principles for switched delay systems,” IMA Journal of Mathematical Control and Information, vol. 28, no. 1, pp. 19–39, 2011.
- X. Liu, “Stabilization of switched linear systems with mode-dependent time-varying delays,” Applied Mathematics and Computation, vol. 216, no. 9, pp. 2581–2586, 2010.
- M. S. Branicky, “Multiple Lyapunov functions and other analysis tools for switched and hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 475–482, 1998.
- S. Pettersson and B. Lennartson, “Stability and robustness for hybrid systems,” in Proceedings of the IEEE Conference on Decision and Control, vol. 12, pp. 1202–1207, 1996.
- D. Boularas and D. Cheban, “Asymptotic stability of switching systems,” Electronic Journal of Differential Equations, vol. 2010, no. 21, pp. 1–18, 2010.
- J. Liu, X. Liu, and W.-C. Xie, “Input-to-state stability of impulsive and switching hybrid systems with time-delay,” Automatica, vol. 47, no. 5, pp. 899–908, 2011.
- V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Practical Stability of Nonlinear Systems, World Scientific, Singapore, 1990.
- J. LaSalle and S. Lefschetz, Stability by Liapunov's Direct Method, with Applications, vol. 4 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1961.
- X. Xu and G. Zhai, “Practical stability and stabilization of hybrid and switched systems,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1897–1903, 2005.
- J. Leth and R. Wisniewski, “On formalism and stability of switched systems,” Journal of Control Theory and Applications, no. 1, pp. 123–130, 2011.
- B. Du and X. Zhang, “Delay-dependent stability analysis and synthesis for uncertain impulsive switched system with mixed delays,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 381571, 9 pages, 2011.
- M. Y. Shieh, J. S. Chiou, and C. M. Cheng, “Delay independence stability analysis and switching law design for the switched time-delay systems,” Information Technology Journal, vol. 10, no. 6, pp. 1201–1207, 2011.
- X. Xu and P. J. Antsaklis, “Practical stabilization of integrator switched systems,” in Proceedings of the American Control Conference, pp. 2767–2772, Denver, Colo, USA, June 2003.
- X. Xu, G. Zhai, and S. He, “On practical asymptotic stabilizability of switched affine systems,” Nonlinear Analysis: Hybrid Systems, vol. 2, no. 1, pp. 196–208, 2008.