Archive of Issues
Russia Izhevsk
Section  Mathematics 
Title  Finite spectrum assignment problem in linear systems with state delay by static output feedback 
Author(s)  Zaitsev V.A.^{a}, Kim I.G.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  We consider a control system defined by a linear timeinvariant system of differential equations with delay $$ \dot x(t)=Ax(t)+A_1x(th)+Bu(t),\quad y(t)=C^*x(t),\quad t>0. \qquad\qquad (1) $$ We construct the controller for the system $(1)$ as linear output feedback $u(t)=Q_0 y(t)+Q_1 y(th)$. We study a finite spectrum assignment problem for the closedloop system. One needs to construct gain matrices $Q_0$, $Q_1$ such that the characteristic quasipolynomial of the closedloop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system $(1)$ under which the criterion was found for solvability of the finite spectrum assignment problem. The obtained result extends to systems with several delays. Corollaries on stabilization by linear static output feedback with delay are obtained for system $(1)$ as well as for systems of type $(1)$ with several delays. 
Keywords  linear delay systems, spectrum assignment, stabilization, output feedback 
UDC  517.929, 517.977 
MSC  93B60, 93B55, 93B52, 93D20, 93C15, 93C05, 34H15 
DOI  10.20537/vm160402 
Received  1 October 2016 
Language  Russian 
Citation  Zaitsev V.A., Kim I.G. Finite spectrum assignment problem in linear systems with state delay by static output feedback, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 463473. 
References 

Full text 