Stabilization of Optimal Dynamic Quantized System with Packet Loss
Mu Li, Lihua Dou, Jie Chen,
and Jian Sun
School of Automation, Beijing Institute of Technology, No.5 Yard, Zhong Guan Cun South Street, Haidian District, Beijing 100081, China
This paper is concerned with the stabilization problem of an optimal dynamic quantized system with packet loss. The optimal dynamic quantizer, which minimizes the quantized output error, is designed for a discretetime system with packet loss occurring in the forward channel. A sufficient condition for the system’s mean square stability is developed based on matrix inequality method. A state feedback controller design method is also proposed, and numerical simulation demonstrates the effectiveness of the proposed method.
-  R. Kalman, “Nonlinear aspects of sampled-data control system,” Proc. Symp. Nonlinear Circuit Theory, Vol.7, 1956.
-  R. Curry, “Estimation and Control With Quantized Measurements,” Proc. Symp. Cambridge, 1970.
-  D. Delchamps, “Stabilizing a linear system with quantized state feedback,” IEEE Trans. on Automatic Control, Vol.35, pp. 916-924, 1990.
-  N. Elia and S. K. Mitter, “Stabilization of linear systems with limited information,” IEEE Trans. on Automatic Control, Vol.46, pp. 1384-1400, 2001.
-  M. Fu and L. Xie, “The sector bound approach to quantized feedback control,” IEEE Trans. on Automatic Control, Vol.50, pp. 1698-1711, 2005.
-  H. Hatmovich, M. M. Seron, and G. C. Goodwin, “Geometric characterization of multivariable quadratically stabilizing quantizers,” Int. J. of Control, Vol.79, pp. 845-857, 2006.
-  H. Ishii and T. Koji, “The Coarsest Logarithmic Quantizers for Stabilization of Linear Systems with Packet Losses,” Proc. of the 46th IEEE Conf. on Decision and Control, pp. 2235-2240, 2007.
-  H. Ishii and T. Koji, “Tradeoffs between quantization and packet loss in networked control of linear systems,” Automatica, Vol.45, pp. 2963-2970, 2009.
-  E. Fridman and M. Dambrine, “Control under quantization, saturation and delay: An LMI approach,” Automatica, Vol.45, pp. 2258-2264, 2009.
-  F. Rasool, D. Huang, and S. K. Nguang, “Robust H∞ output feedback control of networked control systems with multiple quantizers,” J. of the Franklin Institute, Vol.349, pp. 1153-1173, 2012.
-  N. Xiao, M. Fu, and L. Xie , “Stabilization of Markov jump linear systems using quantized state feedback,” Automatica, Vol.46, pp. 1696-1702, 2010.
-  N. Xiao, M. Fu, and L. Xie , “Quantized Stabilization of Markov Jump Linear Systems via State Feedback,” Proc. of American Control Conf., pp. 4020-4025, 2009.
-  R. W. Brockett and D. Liberzon, “Quantized feedback stabilization of linear systems,” IEEE Trans. on Automatic Control, Vol.45, pp. 1279-1289, 2000.
-  D. Liberzon, “Hybrid feedback stabilization of systems with quantized signals,” Automatica, Vol.39, pp. 1543-1554, 2003.
-  S. Azuma and T. Sugie, “Optimal dynamic quantizers for discrete valued input control,” Automatica, Vol.44, pp. 396-406, 2008.
-  S. Azuma and T. Sugie, “An Analytical Solution to Dynamic Quantization Problem of Nonlinear Control Systems,” Proc. of the 48th IEEE Conf. on Decision and Control, 2009, 3914-3919.
-  S. Azuma and T. Sugie, “Stability analysis of optimally quantised LFT feedback systems,” Int. J. of Control, Vol.83, pp. 1125-1135, 2010.