H2/H∞ formulation of LQR controls based on LMI for continuous-time uncertain systems

Rodrigo da Ponte Caun, Edvaldo Assunção and Marcelo Carvalho Minhoto Teixeira

International Journal of Systems Science, 2021, vol. 52, issue 3, 612-634

Abstract: The classical theory of linear matrix inequality (LMI)-based linear quadratic regulator (LQR) control that is well established in literature does not provide, in the controller project phase, the occurrence of exogenous inputs acting on the plants. Therefore, this study proposes sufficient conditions for the robust synthesis of a mixed ${\mathcal H}_2$H2/${\mathcal H}_\infty$H∞ control of the LQR problem. A new mixed polytopic and norm-bounded uncertainties representation for linear time-invariant uncertain systems allows to express different uncertainty models in one single LMI by using the S-procedure. As an additional objective, we propose the study of the robustness of controllers concerned with the sensibility of their coefficients, in such a way that the variations in controller gain matrix are described by norm-bounded uncertainties. A practical implementation in Quanser$^{\circledR}$® active suspension evaluates the control projects through the rejection level of vibrations caused by track irregularities.

Date: 2021
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DOI: 10.1080/00207721.2020.1836283

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