DOI: 10.17586/2226-1494-2017-17-4-658-663


A. S. Pavlov , A. V. Ushakov

Read the full article 
Article in Russian

For citation: Pavlov A.S., Ushakov A.V. Signal discrepancy estimation in equivalent representation problem of discrete system. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2017, vol. 17, no. 4, pp. 658–663 (in Russian). doi: 10.17586/2226-1494-2017-17-4-658-663


Subject of Research.The considered problems are representations of the discrete equivalent description of a continuous system to a discrete description with smaller interval than the original one provided that the zero-order hold devices are used as a memory element in the digital control of continuous system. It is shown that in connection with the above, there is a problem of the signal discrepancy estimation in the task of equivalent representation of these discrete systems. Method. Estimation method of signal discrepancy relies on the capabilities of the state space framework with the use of integral representations of continuous system dynamics equation. The scalar analytical assessment of a signal discrepancy between the initial and transformed systems is created on a difference norm of vectors of stimulated system movement. Main Results. The assessment problem is solved for boundaries of the scalar value interval for signal discrepancy state vectors of the source and resulting systems. Analytical expression for this case is received, and recommendations about the equivalent system formation with a smaller discrete interval are created on its basis. Practical Relevance. The obtained theoretical results can be used in the development and analysis of MIMO discrete systems when the system has different discrete intervals of separate channels.

Keywords: discrete systems, different discrete intervals, scalar value estimation, zero-order hold device, equivalent systems, MIMO systems

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) and the Russian Federation President Grant No.14.Y31.16.9281-НШ.

 1.     Besekerskii V.A. Digital Automatic Systems. Moscow, Nauka Publ., 1976, 576 p. (In Russian)
2.     Solodovnikov V.V., Kon'kov V.G., Sukhanov V.A., Shevyakov O.V. Microprocessor-Based Automatic Control Systems. Basics of Theory and Elements. Moscow, Vysshaya Shkola Publ., 1991, 255 p. (In Russian)
3.     Kuo B.C. Digital Control Systems. Oxford University Press, 1995, 784 p.
4.     Tou J.T. Digital and Sampled-data Control Systems. NY, McGraw-Hill Inc., 1959, 631 p.
5.     Dudarenko N.A., Polyakova M.V., Ushakov A.V. Control of degeneration of discrete multichannel systems with multiple discrete intervals. Optoelectronics, Instrumentation and Data Processing, 2012, vol. 48, no. 5, pp. 66–78.
6.     Bystrov S.V., Grigoriev V.V., Rabysh E.Yu., Cherevko N.A. Exponential stability of continuous dynamic systems. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2011, no. 3, pp. 44–47. (In Russian)
7.     Tou J.T. Modern Control Theory.NY, McGraw-Hill, 1964.
8.     Zadeh L.A., Desoer C.A. Linear System Theory: The State Space Approach. NY, McGraw-Hill, 1963, 628 p.
9.     Shannon C.E. A mathematical theory of communication. Bell System Technical Journal, 1948, vol. 27, pp. 379–423.
10.  Kotel'nikov V.A. On the transmission capacity of ’ether’ and wire in electric communications.Physics-Uspekhi, 2006, vol. 49, pp. 736–744. doi: 10.1070/PU2006v049n07ABEH006160
11.  Tsypkin Ya.Z. Theory of Linear Pulse Systems. Moscow, Fizmatgiz Publ., 1963, 968 p.
12.  Isermann R. Digital Control Systems. V. 1: Fundamentals, Deterministic Control. Springer-Verlag Berlin Heidelberg, 1989, 336 p. doi: 10.1007/978-3-642-86417-9
13.  Jury E.I. Sampled-Data Control Systems. NY, John Wiley & Sons, 1958.
14.  Grigor'ev V.V., Drozdov V.N., Lavrent'ev V.V., Ushakov A.V. Synthesis of Digital Systems Using Computer Controls. Leningrad, Mashinostroenie Publ., 1983, 245 p. (In Russian)
15.  Voevodin V.V., Kuznetsov Yu.A. Matrices and Calculations. Moscow, Nauka Publ., 1984, 320 p.
16.  Xu Jiagu. Lecture Notes on Mathematical Olympiad Courses V. 8. For Senior Section (V. 1). World Scientific, 2012, 260 p.
Copyright 2001-2018 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.