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Avtomatika i Telemekhanika, 2020, Issue 8, Pages 40–53
DOI: https://doi.org/10.31857/S0005231020080048 (Mi at15562) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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Generalized $\mathcal{H}_2$ control of a linear continuous-discrete system on a finite horizon

R. S. Biryukov

Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod, Russia
Full-text PDF (245 kB) Citations (1)
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DOI: https://doi.org/10.31857/S0005231020080048
Abstract: This paper considers a linear continuous-discrete time-varying system described by a set of differential and difference equations on a finite horizon. For such a hybrid system, the concept of the generalized $\mathcal{H}_2$ norm is introduced, representing the induced norm of a linear operator generated by the system under consideration. This norm is characterized in terms of Lyapunov difference equations and also in terms of recursive linear matrix inequalities. Discrete time-varying optimal controllers, including multiobjective ones, that minimize the generalized $\mathcal{H}_2$ norm of the closed loop system are designed.
Keywords: linear time-varying hybrid system, generalized $\mathcal{H}_2$, optimal control, multiobjective optimization.
Funding agency
This work was supported by the Russian Foundation for Basic Research, projects nos. 18-41- 520002, 19-01-00289, project no. 0729-2020-0055, and by the Research and Education Mathematical Center “Mathematics for Future Technologies.”
Presented by the member of Editorial Board: B. T. Polyak

Received: 23.07.2019
Revised: 05.10.2019
Accepted: 30.01.2020
English version:
Automation and Remote Control, 2020, Volume 81, Issue 8, Pages 1394–1404
DOI: https://doi.org/10.1134/S0005117920080032
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. S. Biryukov, “Generalized $\mathcal{H}_2$ control of a linear continuous-discrete system on a finite horizon”, Avtomat. i Telemekh., 2020, no. 8, 40–53; Autom. Remote Control, 81:8 (2020), 1394–1404
Citation in format AMSBIB
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\jour Avtomat. i Telemekh.
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\pages 40--53
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\jour Autom. Remote Control
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\vol 81
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\pages 1394--1404
\crossref{https://doi.org/10.1134/S0005117920080032}
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  • https://www.mathnet.ru/eng/at/y2020/i8/p40
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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