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Analysis and Optimization of Systems pp 130–141Cite as

Conservation de la minimalite par echantillonnage aleatoire

  • Session 13 Linear Systems II
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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 63))

Abstract

The controllability preservation of controlled non stochastic continuous time linear system after discretization has been studied in [6] then in [10], [11], [12].

We study a similar problem : the controllability preservation of a non controlled stochastic linear system when the discretization process is run by renewal process.

This study is concerned with discrete time and set necessary and sufficient conditions for the preservation of minimality of linear system representation:

$$X_{(t + 1)\Delta } = F_\Delta {\mathbf{ }}X_{t\Delta } + {\mathbf{ }}\varepsilon _{t\Delta } {\mathbf{ }};{\mathbf{ }}Y_{t\Delta } = HX_{t\Delta } {\mathbf{ }},{\mathbf{ }}t \in \mathbb{Z}$$

by a renewal process (Tt)t∈ℕ (when Δ is yhe basis sampling step).

Conditions are on the injectivity property of the generating function of (Tt+1−Tt).

We have similar results with continuous time and with unstable systems. They are not included here.

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Author information

Authors and Affiliations

  1. Université Aix-Marseille III GREQF, 41,rue des dominicaines, 13001, Marseille, France

    C. Deniau

  2. Université Paris V Equipe statistique Appliquée Université Paris, Sud. Bât 425, 91405, Orsay-Cédex, France

    G. Oppenmeim & Cl. Viano

Authors
  1. C. Deniau
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  2. G. Oppenmeim
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  3. Cl. Viano
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Editor information

A. Bensoussan J. L. Lions

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© 1984 Springer-Verlag

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Deniau, C., Oppenmeim, G., Viano, C. (1984). Conservation de la minimalite par echantillonnage aleatoire. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 63. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006282

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  • DOI: https://doi.org/10.1007/BFb0006282

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13552-4

  • Online ISBN: 978-3-540-39010-7

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