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A New $H_2$ Bound for $H_{\infty}$ Entropy  

Zhang, Hui (State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Department of Control Science & Engineering, Zhejiang University)
Sun, Youxian (State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Department of Control Science & Engineering, Zhejiang University)
Publication Information
International Journal of Control, Automation, and Systems / v.6, no.4, 2008 , pp. 620-625 More about this Journal
Abstract
The $H_{\infty}$ entropy in $H_{\infty}$ control theory is discussed based on investigating information transmission in continuous-time linear stochastic systems. It is proved that the stabilizing feedback does not change the time-average information transmission between system input and output, and the $H_{\infty}$ entropies of open- and closed-loop stable transfer functions are bounded by mutual information rate between input and output in the open-loop system. Furthermore, a new $H_2$ upper bound for $H_{\infty}$ entropy is introduced with a numerical example. Thus the $H_{\infty}$ entropy of a stable transfer function is sandwiched between $H_2$ norms of the original system and a static feedback system.
Keywords
Feedback; null; null; information transmission; linear stochastic system; mutual information rate;
Citations & Related Records
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Times Cited By Web Of Science : 0  (Related Records In Web of Science)
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1 S. Boyd, Linear Controller Design - Limits of Performance, Prentice-Hall, New Jersey, 1991
2 T. Cover and S. Pombra, "Gaussian feedback capacity," IEEE Trans. on Information Theory, vol. 35, no. 1, pp. 37-43, 1989   DOI   ScienceOn
3 K. Zhou, Essential of Robust Control, Prentice- Hall, New Jersey, 1998
4 T. E. Duncan, "On the calculation of mutual information," SIAM Journal on Applied Mathematics, vol. 19, no. 1, pp. 215-220, 1970   DOI   ScienceOn
5 H. Zhang and Y. X. Sun, "Information theoretic interpretations for $H_\infty$ entropy," Proc. of the 16th IFAC World Congress, Prague, July 3-8, 2005
6 D. P. Palomar and S. Verdú, "Representation of mutual information via input estimates," IEEE Trans. on Information Theory, vol. 53, no. 2, pp. 453-470, 2007   DOI   ScienceOn
7 P. A. Iglesias and M. A. Peters, "An entropy formula for nonlinear systems," International Journal of Franklin Institute, vol. 337, pp. 859- 874, 2000   DOI   ScienceOn
8 M. S. Pinsker, Information and Information Stability of Random Variables and Processes, Holden-Day, Inc., 1964
9 S. Ihara, Information Theory for Continuous Systems, World Scientific Publishing Co. Pte. Ltd., Singapore, 1993
10 S.-H. Lee and J.-S. Kim, "Mixed $H_2/H_\infty$ - controller realization with entropy integral," International Journal of Control, Automation, and Systems, vol. 1, no. 2, pp. 206-209, 2003
11 T. Kailath, Linear Estimation, Prentice Hall, New Jersey, 2000
12 D. Mustafa, K. Glover, Minimum Entropy $H_\infty$ Control, Springer-Verlay, Berlin, 1990
13 A. A. Stoorvogel and J. H. Van Schuppen, "System identification with information theoretic criteria," Identification, Adaptation, Learning (S. Bittanti, G. Picc, Eds.), pp. 289-338, Springer, Berlin, 1996