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Zero Orders and Dimensions of Some Invariant Subspaces in Linear Structured Systems

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Abstract

In this paper we consider linear structured systems which represent a large class of parameter-dependent linear systems and we study invariants for such systems under a large group of transformations including state feedback. In this context we consider the dimension of the maximal output-nulling invariant subspace of a linear structured system, the number and structure of its invariant zeros and its structure at infinity. We give generic characterizations of the invariants in terms of properties of the directed graph that can be naturally associated with a linear structured system.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 000, 2628 CD, Delft, The Netherlands

    J. W. van der Woude

  2. Laboratoire d’Automatique de Grenoble, ENSIEG, INPG, BP 46, 000, 38402, Saint-Martin-d’Heres, France

    C. Commault

  3. Laboratoire d’Automatique de Grenoble, ENSIEG, INPG, BP 46, 000, 38402, Saint-Martin-d’Heres, France

    J. M. Dion

Authors
  1. J. W. van der Woude
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  2. C. Commault
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  3. J. M. Dion
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Corresponding authors

Correspondence to J. W. van der Woude, C. Commault or J. M. Dion.

Additional information

Date received: March 1, 2002. Date revised: April 1, 2003. The first author’s stay at the Laboratoire d’Automatique de Grenoble was supported by grants of the Netherlands Organization for Scientific Research (NWO), the Institut National Polytechnique de Grenoble (INPG) and the French Ministry of Research.

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van der Woude, J., Commault, C. & Dion, J. Zero Orders and Dimensions of Some Invariant Subspaces in Linear Structured Systems. Math. Control Signals Systems 16, 225–237 (2003). https://doi.org/10.1007/s00498-003-0134-8

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  • DOI: https://doi.org/10.1007/s00498-003-0134-8