Stability Analysis of Dynamic Systems in the Polynomial Vector-Matrix Representation

Systems Theory and General Control Theory


This paper suggests frequency-domain stability criteria for homogeneous multiconnected automatic control systems that allow an easy stability analysis of high-order systems of a large dimension. The results are confirmed by mathematical modeling.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. A. Krasovskii et al., Handbook on Automatic Control Theory (Nauka, Moscow, 1987) [in Russian].Google Scholar
  2. 2.
    A. A. Krasovskii, “On automatic regulation processes in one-type bounded linear systems,” Tr. VVIA im. Zhukovskogo, No. 576 (1955).Google Scholar
  3. 3.
    O. S. Sobolev, Studies in Linear Multiconnected Systems (Energoatomizdat, Moscow, 1985) [in Russian].Google Scholar
  4. 4.
    B. T. Polyak and Ya. Z. Tsypkin, “Stability and robust stability of one-type systems,” Avtom. Telemekh., No. 11, 91–104 (1996).MATHGoogle Scholar
  5. 5.
    B. N. Petrov, B. A. Cherkasov, B. G. Il’yasov, and G. G. Kulikov, “Frequency methods of analysis and synthesis of multidimensional automatic regulation systems,” Sov. Phys. Dokl. 24, 528 (1979).MATHGoogle Scholar
  6. 6.
    B. G. Il’yasov and Yu. S. Kabal’nov, “The stability study of multi-connected automatic control systems with holonomic connections between subsystems,” Avtom. Telemekh., No. 8, 82–90 (1995).MATHGoogle Scholar
  7. 7.
    B. G. Il’yasov, G. A. Saitova, and E. A. Khalikova, “Analyzing stability margins of homogeneous MIMO control systems,” J. Comput. Syst. Sci. Int. 48, 502 (2009).CrossRefMATHGoogle Scholar
  8. 8.
    B. G. Il’yasov and G. A. Saitova, “A systems approach to studying multiconnected automated control systems based on frequency methods,” Autom. Remote Control 74, 456 (2013).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Ufa State Aviation Technical UniversityUfaRussia

Personalised recommendations