Skip to main content
SpringerLink
Log in

Design of nonlinear selectively invariant systems based on the controllable Jordan form

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

Abstract

A method to design the nonlinear control systems that are selectively invariant to the unmeasurable bounded perturbations with a certain K(p)-image was proposed. The perturbations may be arbitrary, but their order should not exceed the value established at the design. The nonlinear control is generated relying on the state variables of the extended plant and the estimates of the state variables of a virtual system that is equivalent to the extended plant. A numerical example of design was presented.

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. Gaiduk, A.R., Design of Control Systems with a Given Form of Inputs, Autom. Remote Control, 1984, vol. 45, no. 6, part 1, pp. 692–698.

    MathSciNet  Google Scholar 

  2. Isidori, A. and Byrnes, C.I., Out Regulation of Nonlinear Systems, IEEE Trans. Automat. Control, 1990, vol. 35, no. 2, pp. 131–140.

    Article  MathSciNet  MATH  Google Scholar 

  3. Nikiforov, V.O., Nonlinear Control System with Compensation of the External Deterministic Perturbations, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1997, no. 4, pp. 69–73.

    Google Scholar 

  4. Serrani, A., Isidori, A., and Marconi, L., Semiglobal Nonlinear Output Regulation with Adaptive Internal Model, IEEE Trans. Automat. Control, 2001, vol. 46, no. 8, pp. 1178–1194.

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, Z. and Huang, J., Solution of Output Regulation of Singular Nonlinear Systems by Normal Output Feedback, IEEE Trans. Automat. Control, 2002, vol. 47, no. 5, pp. 808–813.

    Article  MathSciNet  Google Scholar 

  6. Huang, J., Remarks on the Robust Output Regulation Problem for Nonlinear Systems, IEEE Trans. Automat. Control, 2001, vol. 46, no. 12, pp. 2028–2031.

    Article  MathSciNet  MATH  Google Scholar 

  7. Marino, R., Santosuosso, G.L., and Tomei, P., Robust Adaptive Compensation of Biased Sinusoidal Disturbances with Unknown Frequency, Automatica, 2003, vol. 39, pp. 1755–1761.

    Article  MathSciNet  MATH  Google Scholar 

  8. Nikiforov, V.O., Adaptivnoe i robastnoe upravlenie s kompensatsiei vozmushchenii (Adaptive and Robust Control with Compensation of Perturbations), St. Petersburg: Nauka, 2003.

    Google Scholar 

  9. Bobtsov, A.A. and Kremlev, A.S., Algorithm to Compensate Unknown Sinusoidal Perturbation for the Linear Nonminimal-phase Plant, Mekhatronika, Avtomatiz., Upravlen., 2008, no. 10, pp. 14–17.

    Google Scholar 

  10. Aranovskii, S.V., Bobtsov, A.A., and Pyrkin, A.A., Adaptive Observer of an Unknown Sinusoidal Output Disturbance for Linear Plants, Autom. Remote Control, 2009, vol. 70, no. 11, pp. 1862–1870.

    Article  MathSciNet  MATH  Google Scholar 

  11. Bobtsov, A.A. and Kholunin, S.A., Control of Ill-defined Linear Plant with Compensation of External Perturbation, Izv. Vyssh. Uchebn. Zaved., Priborostr., 2005, vol. 48, no. 1, pp. 18–25.

    Google Scholar 

  12. Tsykunov, A.M., Robust Control Algorithms with Compensations of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.

    Article  MathSciNet  MATH  Google Scholar 

  13. Bobtsov, A.A., Adaptive Output Control with Compensation of Shifted Harmonic Perturbation, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2009, no. 1, pp. 45–48.

    Google Scholar 

  14. Nazin, S.A., Polyak, B.T., and Topunov M.V., Rejection of Bounded Exogenous Disturbances by the Method of Invariant Ellipsoids, Autom. Remote Control, 2007, vol. 68, no. 3, pp. 467–486.

    Article  MathSciNet  MATH  Google Scholar 

  15. Bobtsov, A.A., Kremlev, A.S., and Pyrkin, A.A., Compensation of Harmonic Disturbances in Nonlinear Plants with Parametric and Functional Uncertainty, Autom. Remote Control, 2011, vol. 72, no. 1, pp. 111–118.

    Article  MathSciNet  MATH  Google Scholar 

  16. Gaiduk, A.R., Design of Nonlinear Systems Based on the Controllable Jordan Form, Autom. Remote Control, 2006, vol. 67, no. 7, pp. 1017–1027.

    Article  MathSciNet  MATH  Google Scholar 

  17. Gauthier, J., Hammouri, H., and Othman, S., A Simple Observer for Nonlinear Systems: Application to Bioreactors, IEEE Trans. Automat. Control, 1992, vol. 37, no. 6, pp. 875–880.

    Article  MathSciNet  MATH  Google Scholar 

  18. Gaiduk, A.R., Teoriya avtomaticheskogo upravleniya (Automatic Control Theory), Moscow: Vysshaya Shkola, 2010.

    Google Scholar 

  19. Demidovich, B.P., Lektsii po matematicheskoi teorii ustoichivosti (Lectures of the Mathematical Theory of Stability), Moscow: Nauka, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technological Institute of the Federal South University, Taganrog, Russia

    A. R. Gaiduk

Authors
  1. A. R. Gaiduk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.R. Gaiduk, 2013, published in Avtomatika i Telemekhanika, 2013, No. 7, pp. 3–16.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaiduk, A.R. Design of nonlinear selectively invariant systems based on the controllable Jordan form. Autom Remote Control 74, 1061–1071 (2013). https://doi.org/10.1134/S0005117913070011

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117913070011

Keywords

Search

Navigation