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Linear Matrix Inequalities in Control Systems with Uncertainty

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Abstract

The survey deals with the application of linear matrix inequalities to taking into account possible uncertainties (in the system description, exogenous disturbances, and the initial conditions) in the control analysis and synthesis for linear systems.

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Notes

  1. It is well known that if the control and disturbance are applied “at one point,” i.e., the matrices \(B_1\) and \(D \) coincide, then the system output can be made arbitrarily small at the expense of a huge control.

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ACKNOWLEDGMENTS

The authors are grateful to the referees for useful comments and bibliographical recommendations.

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This work was supported by the Russian Foundation for Basic Research, project no. 19-18-50226.

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Correspondence to B. T. Polyak, M. V. Khlebnikov or P. S. Shcherbakov.

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Translated by V. Potapchouck

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Polyak, B.T., Khlebnikov, M.V. & Shcherbakov, P.S. Linear Matrix Inequalities in Control Systems with Uncertainty. Autom Remote Control 82, 1–40 (2021). https://doi.org/10.1134/S000511792101001X

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