Skip to main content
Log in

A Study of Periodic Motions in Homogeneous Nonlinear Multivariable Systems Written in the Polynomial Vector-Matrix Representation

  • SYSTEMS THEORY AND GENERAL CONTROL THEORY
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

In this paper, we suggest a method for estimating the parameters of periodic motions and also a frequency-domain criterion of their stability for nonlinear time-invariant homogeneous (identical) multivariable automatic control systems with structurally identical subsystems. This method can be used to simply determine the parameters of periodic motions and their stability in the class of systems mentioned above based on the structural decomposition and the method of harmonic linearization. The results are confirmed by mathematical modeling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. O. S. Sobolev, Research Methods for Linear Multiply Connected Systems (Energoatomizdat, Moscow, 1985) [in Russian].

    Google Scholar 

  2. B. T. Polyak and Ya. Z. Tsypkin, “Stability and robust stability of similar systems,” Avtom. Telemekh., No. 11, 91–104 (1996).

  3. B. N. Petrov, B. A. Cherkasov, B. G. Il’yasov, and G. G. Kulikov, “Frequency analysis and synthesis of multidimensional automatic control systems,” Dokl. Akad. Nauk SSSR 247, 304–307 (1979).

    MathSciNet  Google Scholar 

  4. B. G. Il’yasov and Yu. S. Kabal’nov, “A study of the stability of the same type of multiply connected automatic control systems with holonomic connections between subsystems,” Avtom. Telemekh., No. 8, 82–90 (1995).

  5. 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).

    Article  Google Scholar 

  6. 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).

    Article  MathSciNet  Google Scholar 

  7. B. G. Il’yasov and G. A. Saitova, “Stability analysis of dynamic systems in the polynomial vector-matrix representation,” J. Comput. Syst. Sci. Int. 57, 171 (2018).

    Article  MathSciNet  Google Scholar 

  8. B. G. Il’yasov, G. A. Saitova, and E. V. Denisova, “Analysis of periodic motions in non-linear, homogeneous, multiply connected automatic control systems (MCACS),” Mekhatron., Avtomatiz., Upravl., No. 7, 29–34 (2001).

  9. B. G. Il’yasov, R. A. Munasypov, G. A. Saitova, et al., “Analysis of periodic motions in multiply connected systems with fuzzy regulators in separate subsystems,” Mekhatron., Avtomatiz., Upravl., No. 8, 24–29 (2004).

  10. S. N. Vasil’ev, B. G. Il’yasov, M. N. Krasil’shchikov, et al., Control Problems of Complex Dynamic Objects of Aviation and Space Technology, Ed. by S. N. Vasil’ev (Mashinostroenie, Moscow, 2015) [in Russian].

    Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project nos. 18-08-00702 A and 17-48-020956 r_a.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. A. Saitova.

Additional information

Translated by A. Mazurov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Il’yasov, B.G., Saitova, G.A. A Study of Periodic Motions in Homogeneous Nonlinear Multivariable Systems Written in the Polynomial Vector-Matrix Representation. J. Comput. Syst. Sci. Int. 59, 1–7 (2020). https://doi.org/10.1134/S1064230719060078

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230719060078

Navigation