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Reachability, observability, and minimality for shift-invariant two-point boundary-value descriptor systems

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Abstract

In this paper we study the system-theoretic properties of two related classes of shift-invariant two-point boundary-value descriptor systems (TPBVDSs), namelydisplacement systems for which Green's function is shift-invariant, andstationary systems for which the input-output map is stationary. For such systems it is possible to obtain detailed characterizations of the properties of weak reachability and observability introduced in [16] and of minimality as well. An important difference, that has also been noted before in a different context [9], is that there is a certain level of nonuniqueness in minimal realizations. Another property that is studied in this paper is that of extendibility, i.e., the concept of considering a TPBVDS as being defined on a sequence of intervals of increasing length. Necessary and sufficient conditions for extendibility are given.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science and Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts, USA

    Ramine Nikoukhah & Alan S. Willsky

  2. Department of Electrical Engineering and Computer Science, University of California, 95616, Davis, California, USA

    Bernard C. Levy

Authors
  1. Ramine Nikoukhah
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  2. Alan S. Willsky
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  3. Bernard C. Levy
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Additional information

The research described in this paper was supported in part by the Air Force Office of Scientific Research under Grant AFOSR-88-0032, in part by the National Science Foundation under Grant ECS-8700903, and in part by the Army Research Office under Grant DAAL03-86-K-0171. The work of A. S. Willsky was also supported by INRIA during his sabbatical at the Institut de Recherche en Informatique et Systèmes Aléatoires, Rennes, France.

Also affiliated with and received support from the Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France.

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Nikoukhah, R., Willsky, A.S. & Levy, B.C. Reachability, observability, and minimality for shift-invariant two-point boundary-value descriptor systems. Circuits Systems and Signal Process 8, 313–340 (1989). https://doi.org/10.1007/BF01598418

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  • DOI: https://doi.org/10.1007/BF01598418

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