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		Badong CHEN,Jinchun HU,Hongbo LI,Zengqi SUN.[en_title][J].Control Theory and Technology,2008,6(3):233~238.[Copy]

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BadongCHEN,JinchunHU,HongboLI,ZengqiSUN
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Received:March 08, 2007Revised:September 17, 2007

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Measuring observability by generalized information theoretic quantities

Badong CHEN, Jinchun HU, Hongbo LI, Zengqi SUN

(State Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, China)

Abstract:

A normalized measure is established to provide the quantitative information about the degree of observability for the discrete-time, stochastically autonomous system. This measure is based on the generalized information theoretic quantities (generalized entropy, mutual information) of the system state and the observations, where the system state can be a discrete or a continuous random vector. Some important properties are presented. For the linear case, the explicit formula for the degree of observability is derived, and the equivalence between the proposed measure and the traditional rank condition is proved. The curves for the degree of observability are depicted in a simple example.

Key words: Stochastic system Observability Information theory