Networked \(H_{\infty }\) control of linear systems with state quantization. (English) Zbl 1126.93338

Peng, Chen; Tian, Yu-Chu

Inf. Sci. 177, No. 24, 5763-5774 (2007).

Summary: This paper addresses the problem of \(H_{\infty }\) controller design for linear systems over digital communication networks. A new model is proposed to describe both the network conditions and the state quantization of the networked control systems in a unified framework. From this model, a quantized state feedback strategy is developed for global and asymptotical stabilization of the networked control systems. The same \(H_{\infty }\) disturbance attenuation level as that in the case without quantization is achieved. Numerical examples are given to demonstrate the effectiveness of the proposed method.

MSC:

93B36	\(H^\infty\)-control
93B52	Feedback control
93D20	Asymptotic stability in control theory
93C05	Linear systems in control theory
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

networked control systems; \(H_{\infty }\) control; quantization; linear matrix inequalities; asymptotic stability; quality of services

References:

[1]	Brockett, R. W.; Liberzon, D., Quantized feedback stabilization of linear systems, IEEE Transactions on Automatic Control, 45, 1279-1289 (2000) · Zbl 0988.93069
[2]	Delvenne, J. C., An optimal quantized feedback strategy for scalar linear systems, IEEE Transactions on Automatic Control, 51, 298-303 (2006) · Zbl 1366.93217
[3]	Delchumps, D. F., Stabilizing a linear system with quantized state feedback, IEEE Transactions on Automatic Control, 35, 916-924 (1990) · Zbl 0719.93067
[4]	Fu, M. Y.; Xie, L. H., The sector bound approach to quantized feedback control, IEEE Transactions on Automatic Control, 50, 1698-1711 (2005) · Zbl 1365.81064
[5]	Hale, J. K.; Verduyn-Lunel, S. M., Introduction to Functional Differential Equations (1993), Springer Verlag: Springer Verlag NewYork · Zbl 0787.34002
[6]	Iwasaki, T.; Skelton, R. E.; Grigoriadis, K. M., A Unified Algebraic Approach to Linear Control Design (1998), Taylor Francis: Taylor Francis London
[7]	Kung, H. Y.; Lin, M. H.; Kuo, F. W., Dynamic QoS queuing control mechanism for multimedia differentiated services, Information Sciences, 176, 3453-3471 (2006)
[8]	Kim, D. S.; Lee, Y. S.; Kwon, W. H.; Park, H. S., Maximum allowable delay bounds of networked control systems, Control Engineering Practice, 11, 1301-1313 (2003)
[9]	Lian, F. L.; Moyne, J. R.; Tilbury, D. M., Performance evaluation of control networks: Ethernet, ControlNet, and DeviceNet, IEEE Control Systems Magazine, 21, 66-83 (2001)
[10]	Libemon, D., Hybrid feedback stabilization of systems with quantized signals, Automatica, 39, 1543-1554 (2003) · Zbl 1030.93042
[11]	Lee, S. Y.; Park, S.; Kim, W. C., An efficient location encoding method for moving objects using hierarchical administrative district and road network, Information Sciences, 177, 832-843 (2007)
[13]	Montestruque, L.; Antsaklis, P. J., Static and dynamic quantization in model-based networked control systems, International Journal of Control, 80, 87-101 (2007) · Zbl 1112.68006
[16]	Tian, Yu-Chu; Yu, Zu-Guo; Fidge, Colin, Multifractal nature of network induced time delay in networked control systems, Physics Letters A, 361, 103-107 (2007) · Zbl 1170.68318
[17]	Tipsuwan, Y.; Chow, M.-Y., On the gain scheduling for networked pi controller over IP network, IEEE Transactions on Mechatronics, 9, 491-498 (2004)
[18]	Wong, Y. C.; Wang, T. P.; Lin, Y. B., Effects of route optimization on out-of-order packet delivery in mobile IP networks, Information Sciences, 169, 263-278 (2005)
[19]	Yue, D.; Han, Q. L.; Peng, C., State feedback controller design of networked control systems, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 51, 640-644 (2004)
[20]	Yue, D.; Peng, C.; Tang, G. Y., Guaranteed cost control of linear systems over networks with state and input quantisations, IEE Proceeding: Control Theory and Application, 153, 658-664 (2006)
[21]	Yu, M.; Wang, L.; Chu, T. G.; Hao, F., Stabilization of networked control systems with data packet dropout and transmission delays: continuous-time case, European Journal of Control, 11, 40-49 (2004) · Zbl 1293.93622
[22]	Yue, D.; Han, Q. L.; Lam, J., Network-based robust \(H_∞\) control of systems with uncertainty, Automatica, 6, 999-1007 (2005) · Zbl 1091.93007