DOI: 10.17586/2226-1494-2017-17-2-269-278


N. A. Vunder, A. S. Pavlov, A. V. Ushakov

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For citation: Vunder N.A., Pavlov A.S., Ushakov A.V. Influence of eigenvectors on trajectories of discrete systems with control signal delay. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2017, vol. 17, no. 2, pp. 269–278 (in Russian). doi: 10.17586/2226-1494-2017-17-2-269-278


Subjectof Study.We present research results of the free motion of discrete linear systems in case of the control signal transmissionto continuous plantwith a delay not exceeding the discreteness interval duration. It was foundthat if the output control signal delay does not exceed the discreteness interval durationthen the dimension of the discrete representation of the continuous plant is increased by one. We consider a class of discrete systems with simple structure state matrix and with the eigenvectors structure such that condition number of their matrix is much greater than one.Method. The problem is solved with the use of vector-matrix formalism of state space method;for that reason the system is presented in vector-matrix form. Analytical assessments of processes in the system arefigured on the norm of state vectorfree motion with the calculation of the condition number of the state matrix eigenvectors matrix. Main Results. It has been found that the ill-conditioned eigenvectors structure of the state matrix may cause significant deviations of free motion trajectories from a monotone decreasing curve. Practical Relevance. These properties of the free motion of discrete systems trajectories are recommended for being kept under supervision, both in the design and the operational phases of systems.

Keywords: discrete system, delay, plant, eigenvectors, deviations, free motion, condition number

Acknowledgements. This work was supported by the Government of the Russian Federation, Grant 074-U01; the Ministry of Education and Science of the Russian Federation, Project 14.Z50.31.0031; the Russian Federation President Grant No.14.Y31.16.9281-НШ.

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