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Regulator Problem for Singular Linear Systems with Constrained Control

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Saturated Control of Linear Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 124))

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Abstract

This chapter solves the problem of controlling singular continuous-time systems with constraints on the control magnitude and its rate, by using state and derivative feedback (proportional-derivative controllers). Necessary and sufficient conditions for positive invariance are proposed. The synthesis of the controller is presented using two methods: an exact method based on non-symmetric Riccati equations and an approximate method based on the solution of equation \(XA+XBX=HX\). An example illustrates the feasibility of the proposed approach. As a particular case, the extension to non-singular systems is also presented.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science Semlalia, University Cadi Ayyad, Marrakech, Morocco

    Abdellah Benzaouia, Fouad Mesquine & Mohamed Benhayoun

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

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Benzaouia, A., Mesquine, F., Benhayoun, M. (2018). Regulator Problem for Singular Linear Systems with Constrained Control. In: Saturated Control of Linear Systems. Studies in Systems, Decision and Control, vol 124. Springer, Cham. https://doi.org/10.1007/978-3-319-65990-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-65990-9_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65989-3

  • Online ISBN: 978-3-319-65990-9

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