
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 4, Pages 445–461
(Mi vuu650)




MATHEMATICS
Control over some asymptotic invariants of twodimensional linear control systems with an observer
A. A. Kozlov^{}, A. D. Burak^{} ^{} Polotsk State University, ul. Blokhina, 29, Novopolotsk, 211440, Belarus
Abstract:
We consider a linear timevarying control system with an observer with locally integrable and integrally bounded coefficients
\begin{gather}
\dot x =A(t)x+ B(t)u, \quad x\in\mathbb{R}^n,\quad u\in\mathbb{R}^m,\quad t\geqslant 0,
y =C^*(t)x, \quad y\in\mathbb{R}^p.
\end{gather}
We study a problem of control over asymptotic invariants for the system closed by linear dynamic output feedback with timevarying coefficients. The research method presented in the paper is based on the construction of a system of asymptotic estimation for the state of the system (1), (2), introduced by R. Kalman. For solving the problem, we use the extension of the notion of uniform complete controllability (in the sense of Kalman) proposed by E.L. Tonkov for systems with coefficients from wider functional classes. The notion of uniform complete observability (in the sense of Tonkov) is given for the system (1), (2). For $n=2$, it is proved that uniform complete controllability and uniform complete observability (in the sense of Tonkov) of the system (1), (2) with locally integrable and integrally bounded coefficients are sufficient for arbitrary assignability of the upper Bohl exponent and of the complete spectrum of the Lyapunov exponents for the system closedloop by linear dynamic output feedback. For the proof, we use the previously established results on uniform global attainability of a twodimensional system (1), closed by linear timevarying static state feedback, under the condition of uniform complete controllability (in the sense of Tonkov) of the openloop system (1).
Keywords:
linear control system with an observer, uniform complete controllability, uniform complete observability, global controllability of asymptotic invariants.
DOI:
https://doi.org/10.20537/vm180402
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Bibliographic databases:
UDC:
517.926, 517.977
MSC: 34D08, 34H05, 93C15 Received: 06.09.2018
Citation:
A. A. Kozlov, A. D. Burak, “Control over some asymptotic invariants of twodimensional linear control systems with an observer”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:4 (2018), 445–461
Citation in format AMSBIB
\Bibitem{KozBur18}
\by A.~A.~Kozlov, A.~D.~Burak
\paper Control over some asymptotic invariants of twodimensional linear control systems with an observer
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 4
\pages 445461
\mathnet{http://mi.mathnet.ru/vuu650}
\crossref{https://doi.org/10.20537/vm180402}
\elib{http://elibrary.ru/item.asp?id=36873363}
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