Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2023, Volume 19, Issue 2, Pages 283–299
DOI: https://doi.org/10.21638/11701/spbu10.2023.213 (Mi vspui584) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Control processes

On the question of a constructive controllability criterion. Pt I. Cyclic invariant subspaces

E. A. Kalininaa, A. M. Kamachkina, N. A. Stepenkoa, G. Sh. Tamasyanbc

a St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
b Mozhaisky Military Space Academy, 13, Zhdanovskaya ul., St. Petersburg, 197082, Russian Federation
c Institute for Problems of Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoy pr. V. O., St. Petersburg, 199178, Russian Federation
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DOI: https://doi.org/10.21638/11701/spbu10.2023.213
Abstract: The rank of the Kalman's controllability matrix of linear systems depends on the bases of the invariant cyclic subspaces of the state matrix generated by the columns of the input matrix. The case of the Jordan form of the state matrix and scalar control is studied in detail. It is shown that the dimension of cyclic subspaces is determined by the index numbers of the first non-zero elements of the coordinate blocks of the columns of the input matrix. The formation of the bases of these subspaces is completely disclosed. Based on this, the basis of the space of a constructive control system is constructed.
Keywords: controllability, system structure, cyclic invariant subspaces.
Funding agency Grant number
Russian Science Foundation 20-71-10032
The results of Section 4 were obtained in the Institute of Problems of Mechanical Engineering, Russian Academy of Sciences with the support of the Russian Science Foundation (project N 20-71-10032).
Received: January 30, 2023
Accepted: April 25, 2023
Document Type: Article
UDC: 517.977.1
MSC: 93B25
Language: Russian
Citation: E. A. Kalinina, A. M. Kamachkin, N. A. Stepenko, G. Sh. Tamasyan, “On the question of a constructive controllability criterion. Pt I. Cyclic invariant subspaces”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 19:2 (2023), 283–299
Citation in format AMSBIB
\Bibitem{KalKamSte23}
\by E.~A.~Kalinina, A.~M.~Kamachkin, N.~A.~Stepenko, G.~Sh.~Tamasyan
\paper On the question of a constructive controllability criterion. Pt~I. Cyclic invariant subspaces
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2023
\vol 19
\issue 2
\pages 283--299
\mathnet{http://mi.mathnet.ru/vspui584}
\crossref{https://doi.org/10.21638/11701/spbu10.2023.213}
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    • This publication is cited in the following 1 articles:
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    		Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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