International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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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)
  • Published : 2008.08.31
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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

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