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Stabilization of Systems with Unsymmetrical Saturated Control: An LMI Approach

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Abstract

This paper deals with the regulator problem for linear continuous-time systems with asymmetric saturations on the control. The main contribution of this work is to extend the available results for symmetrical saturations, in term of LMIs, to systems with asymmetric saturations. Hence, LMIs formalism is obtained for the first time for asymmetrical saturation. New less conservative result on saturation is used. An example is presented to illustrate the obtained results.

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Abbreviations

\(> 0\) :

Positive definite matrix P is denoted by \(P > 0\)

\(*\) :

Symmetric term of the off diagonal elements of a square symmetric matrix

\(\mathbb {I}_m\) :

Identity matrix of dimension \(m\)

\(\zeta \) :

Column vector whose components are all equal to 1

\(\otimes \) :

Kronecker product

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Authors and Affiliations

  1. LAEPT-URAC 28, Faculty of Science Semlalia, University Cadi Ayyad, P.B. 2390, Marrakech, Morocco

    Abdellah Benzaouia, Mohamed Benhayoun & Fouad Mesquine

Authors
  1. Abdellah Benzaouia
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  2. Mohamed Benhayoun
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  3. Fouad Mesquine
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Correspondence to Abdellah Benzaouia.

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Benzaouia, A., Benhayoun, M. & Mesquine, F. Stabilization of Systems with Unsymmetrical Saturated Control: An LMI Approach. Circuits Syst Signal Process 33, 3263–3275 (2014). https://doi.org/10.1007/s00034-014-9786-5

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  • DOI: https://doi.org/10.1007/s00034-014-9786-5

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