RuPAC2016 - List of Authors (Chizhova, O.N.)

Paper	Title	Page
TUPSA024	On Stabilization of Systems of Linear Equations with Linear Increasing Time Delay by Observation	261
	O.N. Chizhova, A.P. Zhabko Saint Petersburg State University, Saint Petersburg, Russia
	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.
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Paper

Title

Page

On Stabilization of Systems of Linear Equations with Linear Increasing Time Delay by Observation

261

O.N. Chizhova, A.P. Zhabko
Saint Petersburg State University, Saint Petersburg, Russia

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.

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reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)