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Avtomatika i Telemekhanika, 2018, Issue 11, Pages 32–46
DOI: https://doi.org/10.31857/S000523100002775-6 (Mi at15041) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Linear Systems

Upper bounds on peaks in discrete-time linear systems

V. N. Ahiyevicha, S. E. Parsegovbc, P. S. Shcherbakovbd

a Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia
b Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
c Skolkovo Institute of Science and Technology, Moscow region, Russia
d Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (725 kB) Citations (18)
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DOI: https://doi.org/10.31857/S000523100002775-6
Abstract: Trajectories of stable linear systems with nonzero initial conditions are known to deviate considerably from the zero equilibrium point at finite time instances. In the paper we analyze transients in discrete-time linear systems and provide upper bounds on deviations (peaks) via use of linear matrix inequalities. An approach to peak-minimizing feedback design is also proposed. An analysis of peak effects for norms of powers of Schur stable matrices is presented and a robust version of the problem is considered. The theory is illustrated by numerical examples.
Keywords: linear discrete-time systems, stability, nonzero initial conditions, transient behavior, upper bounds, linear matrix inequalities, robustness.
Funding agency Grant number
Russian Science Foundation 16-11-10015
This work was supporting by the Russian Science Foundation, project no. 16-11-10015.
Presented by the member of Editorial Board: A. L. Fradkov

Received: 19.04.2018
English version:
Automation and Remote Control, 2018, Volume 79, Issue 11, Pages 1976–1988
DOI: https://doi.org/10.1134/S0005117918110036
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. N. Ahiyevich, S. E. Parsegov, P. S. Shcherbakov, “Upper bounds on peaks in discrete-time linear systems”, Avtomat. i Telemekh., 2018, no. 11, 32–46; Autom. Remote Control, 79:11 (2018), 1976–1988
Citation in format AMSBIB
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\paper Upper bounds on peaks in discrete-time linear systems
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\pages 32--46
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  • https://www.mathnet.ru/eng/at/y2018/i11/p32
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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