Information entropy and state observation of a dynamical system

  • Robert Vallée
Section IV Information Theoretic Approach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 286)


An hereditary linear "observation operator" ℓ gives at instant t an image y(t) of the state x of a dynamical differential linear system whose initial state is known only through a probability distribution with information entropy Hx(to). The information entropy Hy(t) of the probability distribution of y(t) is equal to Hx(to) plus a "dynamical gain fo information entropy" and an "observational gain of information entropy". The dynamical gain involves the trace of the evolution matrix of the system. The observational gain involves ℓ and the fundamental matrix of the system. Special cases are presented, one involving a "generalized Laplace transform with matrix argument".


Probability Distribution State Observation Information Entropy North Holland Publishing Fundamental Matrix 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Robert Vallée
    • 1
  1. 1.Université Paris-NordParis

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