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RIS citation export for TUPSA024: On Stabilization of Systems of Linear Equations with Linear Increasing Time Delay by Observation

TY - CONF
AU - Chizhova, O.N.
AU - Zhabko, A.P.
ED - Kuzin, Maxim
ED - Schaa, Volker RW
TI - On Stabilization of Systems of Linear Equations with Linear Increasing Time Delay by Observation
J2 - Proc. of RuPAC2016, St. Petersburg, Russia, November 21-25, 2016
C1 - St. Petersburg, Russia
T2 - Russian Particle Accelerator Conference
T3 - 25
LA - english
AB - Differential-difference equations with time delay are often used in mathematical models describing the dynamics of beams of the charged particles. For example linear equation of the second order with a constant time delay describes in the smoothed approach dynamics of a beam of the charged particles in synchrotrons with a feedback system. However the time delay cannot always be considered constant. The time proportional delay can occur at acceleration of beams of the charged particles in the cyclotron. It should be noted that such time delay is unbounded and well known approaches are not applicable for stability analysis such systems. The stabilizing control for the system of linear equations could be constructed by the information on a state vector of the system. Sometimes the state vector is unknown but we know some linear combinations of its components. Then there is a problem on construction of the stabilizing control with incomplete information. In this paper we investigate a possibility of stabilization of system of linear equations with time proportional delay by the linear observation. Using the sufficient conditions of asymptotic stability of system of linear equations with linear increasing delay we obtain some conditions of existence of the asymptotic evaluation system of the original system. Then we use the asymptotic evaluation system for the construction of the stabilizing control and derive the sufficient conditions for the existence of such control.
PB - JACoW
CP - Geneva, Switzerland
SP - 261
EP - 263
KW - controls
KW - feedback
KW - synchrotron
KW - acceleration
KW - damping
DA - 2017/02
PY - 2017
SN - 978-3-95450-181-6
DO - 10.18429/JACoW-RuPAC2016-TUPSA024
UR - http://jacow.org/rupac2016/papers/tupsa024.pdf
ER -