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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 684642, 13 pages
Stability Analysis of High-Order Iterative Learning Control for a Class of Nonlinear Switched Systems
1School of Electrical Engineering & Automation, Henan Polytechnic University, Jiaozuo 454003, China
2Henan Provincial Open Laboratory for Control Engineering Key Discipline, Henan Polytechnic University, Jiaozuo 454003, China
Received 22 March 2013; Revised 18 June 2013; Accepted 18 June 2013
Academic Editor: Josef Diblík
Copyright © 2013 Xuhui Bu 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.
- D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59–70, 1999.
- D. Liberzon, Switching in Systems and Control, Systems & Control: Foundations & Applications, Birkhäuser, Boston, Mass, USA, 2003.
- Z. Sun and S. S. Ge, Switched Linear Systems: Control and Design, Springer, New York, NY, USA, 2005.
- D. K. Kim, P. Park, and J. W. Ko, “Output-feedback control of systems over communication networks using a deterministic switching system approach,” Automatica, vol. 40, no. 7, pp. 1205–1212, 2004.
- H. Lin and P. J. Antsaklis, “Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach,” International Journal of Control, vol. 78, no. 18, pp. 1447–1458, 2005.
- R. Horowitz and P. Varaiya, “Control design of an automated highway system,” Proceedings of the IEEE, vol. 88, no. 7, pp. 913–925, 2000.
- P. Antsaklis, “Special issue on hybrid systems: theory and applications-a brief introduction to the theory and applications of hybrid systems.,” Proceedings of the IEEE, vol. 88, no. 7, pp. 887–897, 2000.
- J. P. Hespanha and A. S. Morse, “Switching between stabilizing controllers,” Automatica, vol. 38, no. 11, pp. 1905–1917, 2002.
- H. Ishii and B. A. Francis, “Stabilizing a linear system by switching control with dwell time,” IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 1962–1973, 2002.
- 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.
- A. N. Michel, “Recent trends in the stability analysis of hybrid dynamical systems,” IEEE Transactions on Circuits and Systems. I, vol. 46, no. 1, pp. 120–134, 1999.
- 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.
- J. Zhao and G. M. Dimirovski, “Quadratic stability of a class of switched nonlinear systems,” IEEE Transactions on Automatic Control, vol. 49, no. 4, pp. 574–578, 2004.
- H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009.
- Z. Ji, L. Wang, and X. Guo, “Design of switching sequences for controllability realization of switched linear systems,” Automatica, vol. 43, no. 4, pp. 662–668, 2007.
- D. Cheng, “Controllability of switched bilinear systems,” IEEE Transactions on Automatic Control, vol. 50, no. 4, pp. 511–515, 2005.
- J. P. Hespanha, D. Liberzon, D. Angeli, and E. D. Sontag, “Nonlinear norm-observability notions and stability of switched systems,” IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 154–168, 2005.
- Z. Sun and S. S. Ge, “Analysis and synthesis of switched linear control systems,” Automatica, vol. 41, no. 2, pp. 181–195, 2005.
- H. Liu and Y. Shen, “Asynchronous finite-time stabilisation of switched systems with average dwell time,” IET Control Theory & Applications, vol. 6, no. 9, pp. 1213–1219, 2012.
- Q.-K. Li, J. Zhao, and G. M. Dimirovski, “Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 2, pp. 133–142, 2009.
- Q.-K. Li, J. Zhao, X.-J. Liu, and G. M. Dimirovski, “Observer-based tracking control for switched linear systems with time-varying delay,” International Journal of Robust and Nonlinear Control, vol. 21, no. 3, pp. 309–327, 2011.
- B. Niu and J. Zhao, “Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function,” International Journal of Systems Science, vol. 44, no. 5, pp. 978–985, 2013.
- S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of robots by learning.,” Journal of Robotic Systems, vol. 1, no. 2, pp. 123–140, 1984.
- H. S. Ahn, Y. Chen, and K. L. Moore, “Iterative learning control: brief survey and categorization.,” IEEE Transactions on Systems, Man, and Cybernetics Part C, vol. 37, no. 6, pp. 1099–1121, 2007.
- R. Chi, Z. Hou, and J. Xu, “Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition,” Automatica, vol. 44, no. 8, pp. 2207–2213, 2008.
- M. Sun and D. Wang, “Initial shift issues on discrete-time iterative learning control with system relative degree,” IEEE Transactions on Automatic Control, vol. 48, no. 1, pp. 144–148, 2003.
- Z. Hou, J.-X. Xu, and J. Yan, “An iterative learning approach for density control of freeway traffic flow via ramp metering,” Transportation Research Part C, vol. 16, no. 1, pp. 71–97, 2008.
- W. Chen, J. Li, and J. Li, “Practical adaptive iterative learning control framework based on robust adaptive approach,” Asian Journal of Control, vol. 13, no. 1, pp. 85–93, 2011.
- W. Chen and L. Zhang, “Adaptive Iterative learning control for nonlinearly parameterized systems with unknown time-varying delays,” International Journal of Control, Automation and Systems, vol. 8, no. 2, pp. 177–186, 2010.
- X. Bu, F. Yu, Z. Hou, and F. Wang, “Iterative learning control for a class of nonlinear systems with random packet losses,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 567–580, 2013.
- S. Andrei, J. Diblik, K. Denys, and M. Ruzickova, “Stabilization of Lur'e-type nonlinear control systems by Lyapunov-Krasovskii functionals,” Advances in Difference Equations, vol. 2012, 9 pages, 2012.
- I. A. Dzhalladova, J. Baštinec, J. Diblík, and D. Y. Khusainov, “Estimates of exponential stability for solutions of stochastic control systems with delay,” Abstract and Applied Analysis, vol. 2011, Article ID 920412, 14 pages, 2011.
- J. Diblík, D. Ya. Khusainov, and M. Růžičková, “Controllability of linear discrete systems with constant coefficients and pure delay,” SIAM Journal on Control and Optimization, vol. 47, no. 3, pp. 1140–1149, 2008.
- Y. Chen, Z. Gong, and C. Wen, “Analysis of a high-order iterative learning control algorithm for uncertain nonlinear systems with state delays,” Automatica, vol. 34, no. 3, pp. 345–353, 1998.
- T. M. Flett, Differential Analysis, Cambridge University Press, Cambridge, UK, 1980.
- Y. Shen and J. Wang, “Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters,” IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1857–1862, 2007.
- Y. Shen and J. Wang, “Almost sure exponential stability of recurrent neural networks with Markovian switching,” IEEE Transactions on Neural Networks, vol. 20, no. 5, pp. 840–855, 2009.
- Y. Shen and J. Wang, “Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances,” IEEE Transactions on Neural Network, vol. 23, no. 1, pp. 87–96, 2012.
- S. S. Saab, W. G. Vogt, and M. H. Mickle, “Learning control algorithms for tracking “slowly” varying trajectories,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 27, no. 4, pp. 657–670, 1997.
- D. Wang, “Convergence and robustness of discrete time nonlinear systems with iterative learning control,” Automatica, vol. 34, no. 11, pp. 1445–1448, 1998.