Abstract
This paper addresses the stabilization problem for a class of nonlinear systems. It is assumed that the controller can only receive the transmitted sequence of finite coded signals via a limited digital communication channel. Both state and output feedback coder-decoder-controller procedures are proposed. Stabilization conditions involving the size of coding alphabet, the sampling period, system state growth rate and data packet dropout rate are obtained. Finally, an example is given to illustrate the design procedures and effectiveness of the proposed results.
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M. Yu, L. Wang, T. Chu, et al. Modelling and control of networked systems via jump system approach[J]. IET Control Theory and Applications, 2008, 2(6): 535–541.
W. Zhang, L. Yu. Output feedback stabilization of networked control systems with packet dropouts[J]. IEEE Transactions on Automatic Control, 2007, 52(9): 1705–1710.
J. Xiong, J. Lam. Stabilization of linear systems over networks with bounded packet loss[J]. Automatica, 2007, 43(1): 80–87.
S. Hu, W. Yan. Stability robustness of networked control systems with respect to packet loss[J]. Automatica, 2007, 43(7): 1243–1248.
D. Yue, C. Peng, G. Tang. Guaranteed cost control of linear systems over networks with state and input quantizations[J]. IEE Proceedings-Control Theory and Applications, 2006, 153(6): 658–664.
L. Zhou, X. Xiao, G. Lu. Stabilization for networked control systems with nonlinear perturbation[C]//Proceedings of the 17th World Congress The International Federation of Automatic Control. Berlin: Springer-Verlag, 2008: 12570–12574.
X. Zhang, G. Lu, Y. Zheng. Stabilization of networked stochastic time-delay fuzzy systems with data dropout[J]. IEEE Transactions on Fuzzy Systems, 2008, 16(3): 798–807.
E. Tian, D. Yue, C. Peng. Quantized output feedback control for networked control systems[J]. Information Sciences, 2008, 178(12): 2734–2749.
G. N. Nair, F. Fagnani, S. Zampieri, et al. Feedback control under data rate constraints: An overview[J]. Proceedings of the IEEE, 2007, 95(1): 108–137.
L. A. Montestruque, P. J. Antsaklis. Static and dynamic quantization in model-based networked control systems[J]. International Journal of Control, 2007, 80(1): 87–101.
W. S. Wong, R. W. Brockett. Systems with finite communication bandwidth constraints-Part II: Stabilization with limited information feedback[J]. IEEE Transactions on Automatic Control, 1999, 44(5): 1049–1053.
N. Elia, S. K. Mitter. Stabilization of linear lystems with limited information[J]. IEEE Transactions on Automatic Control, 2001, 46(9): 1384–1400.
M. Fu, L. Xie. The sector bound approach to quantized feedback control[J]. IEEE Transactions on Automatic Control, 2005, 50(11): 1698–1712.
H. Gao, T. Chen. A new approach to quantized feedback control systems[J]. Automatica, 2008, 44(2): 534–542.
R. W. Brockett, D. Liberzon. Quantized feedback stabilization of linear systems[J]. IEEE Transactions on Automatic Control, 2000, 45(7): 1279–1289.
D. Liberzon. On stabilization of linear systems with limited information[J]. IEEE Transactions on Automatic Control, 2003, 48(2): 304–307.
A. V. Savkin, T. Cheng. Detectability and output feedback stabilizability of nonlinear networked control systems[J]. IEEE Transactions on Automatic Control, 2007, 52(4): 730–735.
G. Lu, D. W. C. Ho. Full-order and reduced-order observer for Lipschitz descriptor systems: The unified LMI approach[J]. IEEE Transactions on Circuits and Systems-II, 2006, 53(7): 563–567.
G. Lu, D. W. C. Ho. Generalized quadratic stabilization for discrete-time singular systems with time-delay and nonlinear perturbation[J]. Asian Journal of Control, 2005, 7(3): 211–222.
W. Yan, J. Lam. On quadratic stability of systems with structured uncertainty[J]. IEEE Transactions on Automatic Control, 2001, 46(11): 1799–1805.
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This work was supported by the National Natural Science Foundation of China (No.60874021, 60974016), the National Natural Science Foundation of Jiangsu Province (No.BK2007061), Qing Lan Project from the Jiangsu Provincial Department for Education and the National Natural Science Foundation of Nantong University (No.08Z001).
Lei ZHOU received the B.S. and M.S. degrees from the Department of Mathematics, XuZhou Normal University, China, in 2001 and 2004, respectively. He joined Nantong University, Jiangsu, China, in 2004. Currently, he is a Ph.D. candidate of the Department of Mathematics, East China Normal University. His current research interests include nonlinear signal processing, descriptor system control and networked control.
Guoping LU received the B.S. degree from the Department of Applied Mathematics, Chengdu University of Science and Technology, China, in 1984 and the M.S. and Ph.D. degrees from the Department of Mathematics, East China Normal University, China, in 1989 and 1998, respectively. He is currently a professor at the College of Electrical Engineering, Nantong University, Jiangsu, China. His current research interests include nonlinear signal processing, robust control and networked control.
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Zhou, L., Lu, G. Stabilization for nonlinear systems via a limited capacity communication channel with data packet dropout. J. Control Theory Appl. 8, 111–116 (2010). https://doi.org/10.1007/s11768-010-9189-5
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DOI: https://doi.org/10.1007/s11768-010-9189-5