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Global Stability Analysis of Nonlinear Sampled-Data Systems Using Convex Methods

  • Chapter
Delay Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 1))

Abstract

In this chapter, we consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we use a recently introduced Lyapunov approach to derive stability conditions for both the case of fixed sampling period (synchronous) and the case of a time-varying sampling period (asynchronous). This approach requires the existence of a Lyapunov function which decreases over each sampling interval. To enforce this constraint, we use a form of slack variable which exists over the sampling period, may depend on the sampling period, and allows the Lyapunov function to be temporarily increasing. The resulting conditions are enforced using a new method of convex optimization of polynomial variables known as Sum-of-Squares. We use several numerical examples to illustrate this approach.

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Author information

Authors and Affiliations

  1. Arizona State University, P.O. Box 876106, Tempe, AZ, 85287, USA

    Matthew M. Peet

  2. CNRS, LAAS, 7 avenue du Colonel Roche, 31077, Toulouse, France

    Alexandre Seuret

  3. Univ. de Toulouse, LAAS, F-31400, Toulouse, France

    Alexandre Seuret

Authors
  1. Matthew M. Peet
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  2. Alexandre Seuret
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Corresponding author

Correspondence to Matthew M. Peet .

Editor information

Editors and Affiliations

  1. Dept. of Instrumentation & Control Eng. Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic

    Tomáš Vyhlídal

  2. Institut de Recherche en Communications et Cybernétique de Nantes, Nantes Cedex 3, France

    Jean-François Lafay

  3. Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts, USA

    Rifat Sipahi

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Peet, M.M., Seuret, A. (2014). Global Stability Analysis of Nonlinear Sampled-Data Systems Using Convex Methods. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_16

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  • DOI: https://doi.org/10.1007/978-3-319-01695-5_16

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01694-8

  • Online ISBN: 978-3-319-01695-5

  • eBook Packages: EngineeringEngineering (R0)

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