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Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback

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  • Junchao Ren
  • Qingling Zhang

Abstract

This article deals with the problem of normalisation and positive real control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is quadratically normal and quadratically stable (QNQS) and the closed-loop transfer function is extended strictly positive real (ESPR). We first present a new linear matrix inequality (LMI) characterisation of positive realness for normal descriptor systems. This new characterisation provides a kind of decoupling among the Lyapunov matrix, the system matrix and the derivative matrix. Based on this, a necessary and sufficient condition for the desired PD controllers is given and a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

Suggested Citation

  • Junchao Ren & Qingling Zhang, 2013. "Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(3), pages 450-460.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:3:p:450-460
    DOI: 10.1080/00207721.2011.602481
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    Cited by:

    1. Taha H. S. Abdelaziz, 2017. "Pole assignment of multivariable systems using proportional-derivative state feedback," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2871-2886, October.
    2. Xin-zhuang Dong, 2014. "Admissibility analysis of linear singular systems via a delta operator method," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(11), pages 2366-2375, November.
    3. Jian Li & Qingling Zhang & Junchao Ren & Yanhao Zhang, 2017. "Robust decentralised stabilisation of uncertain large-scale interconnected nonlinear descriptor systems via proportional plus derivative feedback," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 2997-3006, October.

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