Skip to main content
SpringerLink
Log in

Conditions for stability and roughness of the distributed plant control system with a controller close to the degenerate system

  • Nonlinear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Conditions for stability and roughness of a distributed plant control system with a controller close to the degenerate system (Schipanov’s controller) were considered. The given operator relations between the plant output and controller are used for mathematical description of the plant and controller. For the linear plant, conditions were given for close-to-invariant behavior of the plant output. For the nonlinear control-linear plant, conditions for boundedness of the plant output, upper bound of the norm of the “action-output,” and the sufficient condition providing closeness of the output behavior to the invariant one were given.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Schipanov, G.V., Theory, Calculation, and Methods of Designing the Automatic Controllers, in G.V. Schipanov i teoriya invariantnosti (G.V. Schipanov and the Invariance Theory), Moscow: Fizmatlit, 2004, pp. 20–140.

    Google Scholar 

  2. Schipanov, G.V., Theory and Methods of Design of the Automatic Controllers, in G.V. Schipanov i teoriya invariantnosti (G.V. Schipanov and the Invariance Theory), Moscow: Fizmatlit, 2004, pp. 141–164.

    Google Scholar 

  3. Petrov, B.N., Izbrannye trudy, tom 1: Teoriya avtomaticheskogo upravleniya (Selected Works, vol. 1: Automatic Control Theory), Moscow: Nauka, 1983.

    Google Scholar 

  4. Solnechnyi, E.M., Degenerate Systems and Their Use in the Problem of Designing the Given Behavior, Moscow: Nauka, 1989.

    Google Scholar 

  5. Gaiduk, A.R., Teoriya i metody analiticheskogo sinteza sistem avtomaticheskogo upravleniya (polinomial’nyi podkhod) (Theory and Methods of Analytical Design of Automatic Control Systems (A Polynomial Approach)), Moscow: Fizmatlit, 2012.

    Google Scholar 

  6. Solnechnyi, E.M., Using G.P. Shchipanov’s Ideas to Provide Perturbation-invariance of the Output of a Distributed Linear Plant, Autom. Remote Control, 2014, vol. 75, no. 1, pp. 75–86.

    Article  MathSciNet  MATH  Google Scholar 

  7. Letov, A.M., Ustoichivost’ nelineinykh reguliruemykh sistem (Stability of Nonlinear Controllable Systems), Moscow: GITTL, 1955.

    Google Scholar 

  8. Gajewski, H., Gröger, K., and Zacharias, K., Nichtlineare operatorgleichungen und Operatordifferentialgleichungen Berlin: Akademie-Verlag, 1974. Translated under the title Nelineinye operatornye uravneniya i operatornye differentsial’nye uravneniya, Moscow: Nauka, 1978.

    MATH  Google Scholar 

  9. Vladimirov, V.S., Obobshchennye funktsii v matematicheskoi fizike (Generalized Functions in Mathematical Physics), Moscow: Nauka, 1976.

    Google Scholar 

  10. Lavrent’ev, M.A. and Shabat, B.V., Metody teorii funktsii kompleksnogo peremennogo (Methods of the Theory of Complex Variables), Moscow: Fizmatgiz, 1958.

    MATH  Google Scholar 

  11. Solnechnyi, E.M. and Cheryomushkina, L.A., On Stability Conditions of a Control System for a Linear Heat Transfer Object Bounded from One Side, Autom. Remote Control, 2011, vol. 72, no. 4, pp. 684–698.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    E. M. Solnechnyi

Authors
  1. E. M. Solnechnyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. M. Solnechnyi.

Additional information

Original Russian Text © E.M. Solnechnyi, 2017, published in Avtomatika i Telemekhanika, 2017, No. 7, pp. 86–94.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Solnechnyi, E.M. Conditions for stability and roughness of the distributed plant control system with a controller close to the degenerate system. Autom Remote Control 78, 1243–1250 (2017). https://doi.org/10.1134/S0005117917070062

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117917070062

Keywords

Search

Navigation