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Asymptotic Properties of Stochastic Delay Systems

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Advances in Time-Delay Systems

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 38))

Abstract

A gentle and elementary introduction to the theory of stochastic lime delay systems is presented in this contribution. First an introduction to the stability problem in the discrete case is given. This class of systems is simpler from a dynamical point of view, as they remain finite dimensional, and provide thus a ‘wann-up’ for what is to come. Since continuous time stochastic systems are analyzed in the language of Itô-calculus, an elementary introduction to the latter is included to make these notes self-contained. Delay-independent and delay dependent conditions for stochastic stability arc derived. Some of these are new. In the absence of equilibria, invariant distributions may still exist. Existence conditions, and the stationary Fokker-Planck equation are discussed. These results are further extended to the class of stochastic neutral systems. Finally. a new realistic design procedure is suggested for dynamic controllers in the absence of precise delay information.

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Authors and Affiliations

  1. School of ECE, Georgia Institute of Technology, Atlanta, GA, 30332-0250

    Erik I. Verriest

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  1. Erik I. Verriest
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  1. Centre de Recherche de Royallieu, Universite de Technologie de Compiègne, UMR CNRS 6022, 60205, Compiègne, France

    Silviu-Iulian Niculescu

  2. Department of Mechanical and Industrial Engineering, Southern Illinois University, Edwardsville, IL, 62025-1805, USA

    Keqin Gu

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Verriest, E.I. (2004). Asymptotic Properties of Stochastic Delay Systems. In: Niculescu, SI., Gu, K. (eds) Advances in Time-Delay Systems. Lecture Notes in Computational Science and Engineering, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18482-6_28

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  • DOI: https://doi.org/10.1007/978-3-642-18482-6_28

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  • Print ISBN: 978-3-540-20890-7

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