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Stability and Stabilization of Linear Systems with Saturating Actuators pp 185–208Cite as

Analysis via the Regions of Saturation Model

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Abstract

This chapter deals with the problem of stability analysis of linear control systems with input saturations using the regions of saturation model. It is shown that considering such a representation for the closed-loop system it is possible to derive necessary and sufficient conditions to ensure that a polyhedral region in the state space is a region of asymptotic stability. These conditions can be tested by linear programming algorithms. The determination of ellipsoidal regions of stability is also presented. In this case only sufficient conditions can be derived. From these conditions, LMI-based optimization problems are proposed to generate regions of asymptotic stability.

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Notes

  1. 1.

    Recall that the symbols “⪯” and “⪰” denote componentwise inequalities.

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Authors and Affiliations

  1. Laboratoire Analyse et Architecture des Systèmes (LAAS), CNRS, av. du Colonel Roche 7, 31077, Toulouse CX 4, France

    Sophie Tarbouriech & Isabelle Queinnec

  2. Laboratoire Analyse et Architecture des Systèmes (LAAS), CNRS, av. du Colonel Roche, 31077, Toulouse CX 4, France

    Germain Garcia

  3. Departamento de Engenharia Elétrica, Universidade Federal do Rio Grande do Sul, av. Osvaldo Aranha 103, 90035-190, Porto Alegre, Rio Grande do Sul, Brazil

    João Manoel Gomes da Silva Jr.

Authors
  1. Sophie Tarbouriech
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  2. Germain Garcia
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  3. João Manoel Gomes da Silva Jr.
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  4. Isabelle Queinnec
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Corresponding author

Correspondence to Sophie Tarbouriech .

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© 2011 Springer-Verlag London Limited

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Tarbouriech, S., Garcia, G., Gomes da Silva, J.M., Queinnec, I. (2011). Analysis via the Regions of Saturation Model. In: Stability and Stabilization of Linear Systems with Saturating Actuators. Springer, London. https://doi.org/10.1007/978-0-85729-941-3_4

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  • DOI: https://doi.org/10.1007/978-0-85729-941-3_4

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-940-6

  • Online ISBN: 978-0-85729-941-3

  • eBook Packages: EngineeringEngineering (R0)

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