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Mathematical systems theory: Causality

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Abstract

The concept of state is studied in a new set-theoretic formalism for systems theory. Starting with the notion of a time system as a set of ordered pairs of abstract time functions, the concepts of (i) non-anticipation and (ii) causality are introduced. It is proved that the class of causal systems (those possessing a set of states and functional state transitions) is precisely the class of non-anticipatory systems. It is shown that every causal system has a series decomposition consisting of a transition system followed by a static system. It is proved that a state set for a causal system is always constructible using a class of “natural” partitions of the system input set. This latter construction generalizes the result known for certain functional discrete systems to a much more general situation.

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Authors and Affiliations

  1. Case Institute of Technology, Cleveland, Ohio, USA

    T. G. Windeknecht

Authors
  1. T. G. Windeknecht
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Additional information

The author gratefully acknowledges the contribution of M. D. Mesarović to this paper. The research has been supported in part by the Office of Naval Research (Contract No. Nonr 1141(12)).

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Windeknecht, T.G. Mathematical systems theory: Causality. Math. Systems Theory 1, 279–288 (1967). https://doi.org/10.1007/BF01695163

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  • DOI: https://doi.org/10.1007/BF01695163

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