Abstract:
A linear control system defined by a stationary differential equation with one lumped and one distributed delay is considered.
In the system, the input is a linear combination of m variables and their derivatives of order not more than n−p and the output is a k-dimensional vector of linear combinations of the state and its derivatives of order not more than p−1. For this system, a spectrum assignment problem by linear static output feedback with delays is studied. Necessary and sufficient conditions are obtained for solvability of the arbitrary spectrum assignment problem by static output feedback controller of the same type as the system. Corollaries on stabilization of the system are obtained.
This work was funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of state assignment No. 075-00232-20-01, project 0827-2020-0010 “Development of the theory and methods of control and stabilization of dynamical systems”.
Citation:
V. A. Zaitsev, I. G. Kim, “Spectrum assignment and stabilization of linear differential equations with delay by static output feedback with delay”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:2 (2020), 208–220
\Bibitem{ZaiKim20}
\by V.~A.~Zaitsev, I.~G.~Kim
\paper Spectrum assignment and stabilization of linear differential equations with delay by static output feedback with delay
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 2
\pages 208--220
\mathnet{http://mi.mathnet.ru/vuu720}
\crossref{https://doi.org/10.35634/vm200205}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000556724800005}
Linking options:
https://www.mathnet.ru/eng/vuu720
https://www.mathnet.ru/eng/vuu/v30/i2/p208
This publication is cited in the following 3 articles:
V. Zaitsev, I. Kim, “Arbitrary coefficient assignment by static output feedback for linear differential equations with non-commensurate lumped and distributed delays”, Mathematics, 9:17 (2021), 2158
I. G. Kim, “Naznachenie konechnogo spektra v lineinykh sistemakh s neskolkimi sosredotochennymi i raspredelennymi zapazdyvaniyami posredstvom staticheskoi obratnoi svyazi po vykhodu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:3 (2020), 367–384
V. A. Zaitsev, I. G. Kim, “Naznachenie spektra v lineinykh sistemakh s neskolkimi soizmerimymi sosredotochennymi i raspredelennymi zapazdyvaniyami v sostoyanii posredstvom staticheskoi obratnoi svyazi po vykhodu”, Izv. IMI UdGU, 56 (2020), 5–19
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