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Control synthesis for polynomial discrete-time systems under input constraints via delayed-state Lyapunov functions

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  • J.L. Pitarch
  • A. Sala
  • J. Lauber
  • T.M. Guerra

Abstract

This paper presents a discrete-time control design methodology for input-saturating systems using a Lyapunov function with dependence on present and past states. The approach is used to bypass the usual difficulty with full polynomial Lyapunov functions of expressing the problem in a convex way. Also polynomial controllers are allowed to depend on both present and past states. Furthermore, by considering saturation limits on the control action, the information about the relationship between the present and past states is introduced via Positivstellensatz multipliers. Sum-of-squares techniques and available semi-definite programming (SDP) software are used in order to find the controller.

Suggested Citation

  • J.L. Pitarch & A. Sala & J. Lauber & T.M. Guerra, 2016. "Control synthesis for polynomial discrete-time systems under input constraints via delayed-state Lyapunov functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1176-1184, April.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:5:p:1176-1184
    DOI: 10.1080/00207721.2014.915357
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    References listed on IDEAS

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    1. Ali Koshkouei & Keith Burnham, 2011. "Adaptive backstepping sliding mode control for feedforward uncertain systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 1935-1946.
    2. Antonio Gonzalez & Antonio Sala & Pedro Garcia & Pedro Albertos, 2013. "Robustness analysis of discrete predictor-based controllers for input-delay systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(2), pages 232-239.
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