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Hybrid Dynamical Systems pp 59–101Cite as

Realization Theory of Linear Hybrid Systems

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 457))

Abstract

This chapter presents a survey on realization theory for linear hybrid systems. Recall that for linear systems, realization theory addresses the problem of existence and minimality of a linear time-invariant state-space representation of an input–output map (transfer function). The results of linear realization theory have turned out to be useful for control synthesis, model reduction, and system identification. In this chapter, we address a similar problem for linear hybrid systems and linear switched systems. We will also discuss the implications of realization theory for estimation and control of hybrid systems.

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Notes

  1. 1.

    Two columns are considered equal, if all their respective entries are equal.

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Author information

Authors and Affiliations

  1. Department of Automatic Control and Computer Science, Ecole des Mines de Douai, 941, rue Charles Bourseul, 59508, Douai, France

    Mihaly Petreczky

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  1. Mihaly Petreczky
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Correspondence to Mihaly Petreczky .

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Editors and Affiliations

  1. LAMIH CNRS UMR 8201, University of Valenciennes and Hainaut-Cambresis, Valenciennes, France

    Mohamed Djemai

  2. LAMIH UMR-CNRS 8201, University of Valenciennes and Hainaut-Cambresis, Valenciennes, France

    Michael Defoort

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Petreczky, M. (2015). Realization Theory of Linear Hybrid Systems. In: Djemai, M., Defoort, M. (eds) Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 457. Springer, Cham. https://doi.org/10.1007/978-3-319-10795-0_3

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  • DOI: https://doi.org/10.1007/978-3-319-10795-0_3

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