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Optimization of Bilinear Control Systems Subjected to Exogenous Disturbances. II. Design

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Abstract

We obtain and discuss new results related to control design for bilinear systems subjected to arbitrary bounded exogenous disturbances. A procedure for the construction of the stabilizability ellipsoid and the domain of stabilizability for bilinear control systems is proposed and its efficiency is proved. This problem is solved both in continuous and discrete time. The main tool is the linear matrix inequality technique. This simple yet general approach is of great potential and can be widely generalized; for instance, to various robust statements of the problem.

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Acknowledgments

This work was partially supported by the Russian Foundation for Basic Research, project no. 18-08-00140. The author would like to thank B.T. Polyak for his interest in this work, fruitful discussions, and useful suggestions.

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  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    M. V. Khlebnikov

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  1. M. V. Khlebnikov
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Correspondence to M. V. Khlebnikov.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 8, pp. 29–43.

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Khlebnikov, M.V. Optimization of Bilinear Control Systems Subjected to Exogenous Disturbances. II. Design. Autom Remote Control 80, 1390–1402 (2019). https://doi.org/10.1134/S0005117919080022

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