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

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


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.


Uncertain repetitive processes Robust stability and stabilization Linear matrix inequalities Finite frequency domain 



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


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Control and Computation EngineeringUniversity of Zielona GóraZielona GóraPoland
  2. 2.Institute of Automation, Electronic and Electrical EngineeringUniversity of Zielona GóraZielona GóraPoland
  3. 3.School of Electronics and Computer ScienceUniversity of SouthamptonSouthamptonUK

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