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A New LMI-Based Controller Design Method for Uncertain Differential Repetitive Processes

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Book cover Advanced, Contemporary Control

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1196))

Abstract

The paper develops new results on stability analysis and control law design for differential linear repetitive processes. These results are based on new dilated LMI characterizations for stability along the pass where auxiliary slack variables with full structure are employed. This provides additional flexibility to the solution. The results are also easily extended to processes with norm-bounded uncertainties. It is also shown that the generalized Kalman-Yakubovich-Popov lemma can be used to obtain stability and controller design procedures in which performance specifications are imposed over finite frequency ranges. Sufficient conditions for the existence of a robust controller in this setting are established. Finally, a simulation example is given to illustrate the merits of the new design.

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Acknowledgments

This work is partially supported by National Science Centre in Poland, grant No. 2017/27/B/ST7/01874.

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Authors and Affiliations

  1. Institute of Control and Computation Engineering, University of Zielona Góra, Szafrana 2, 65-516, Zielona Góra, Poland

    Robert Maniarski

  2. Institute of Automation, Electronic and Electrical Engineering, University of Zielona Góra, Szafrana 2, 65-516, Zielona Góra, Poland

    Wojciech Paszke

  3. School of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK

    Eric Rogers

Authors
  1. Robert Maniarski
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  2. Wojciech Paszke
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  3. Eric Rogers
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Corresponding author

Correspondence to Robert Maniarski .

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Editors and Affiliations

  1. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Andrzej Bartoszewicz

  2. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Jacek Kabziński

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Maniarski, R., Paszke, W., Rogers, E. (2020). A New LMI-Based Controller Design Method for Uncertain Differential Repetitive Processes. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_16

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