On Representations of Abstract Systems with Partial Inputs and Outputs

  • Ievgen Ivanov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8402)


We consider a class of mathematical models called blocks which generalize some input-output models which appear in mathematical systems theory, control theory, signal processing. A block maps partial functions of time to nonempty sets of partial functions of time. A class of strongly nonanticipative blocks can be considered as an analog of the class of causal time systems studied by M. Mesarovic and Y. Takahara. The behavior of a strongly nonanticipative block can be represented using an abstract dynamical system called Nondeterministic Complete Markovian System (NCMS) which is close to the notion of a solution system by O. Hájek. We show that conversely, each initial input-output NCMS (i.e. NCMS with inputs and outputs) is a representation of a strongly nonanticipative block. This result generalizes a link between causality and the existence of state-space representations that exists in several variants of mathematical systems theory to models with partial inputs and outputs.


input-output system signal time partial function state space dynamical system representation 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ievgen Ivanov
    • 1
  1. 1.Université Paul SabatierToulouseFrance

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