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A normalized measure is established to provide the quantitative information about the degree of observabil-ity 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.
A normalized measure is established to provide the quantitative information about the degree of observabil-ity 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.