Median control of continuous dynamic plants with interval parameters

  • T. A. Akunov
  • O. V. Slita
  • S. A. Sudarchikov
  • A. V. Ushakov
Control in Stochastic Systems and Under Uncertainty Conditions


An algorithm for the synthesis of median modal control of a plant with parametric uncertainties given in interval form is proposed. It is supplemented by the check of relative interval estimate of the system state matrix, that ensures the required interval estimate of the quality indices. The results are illustrated by an example.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Ackermann, Robust Control Systems with Uncertain Physical Parameters (Springer, London, 1993).MATHGoogle Scholar
  2. 2.
    I. V. Miroshnik, V. O. Nikiforov, and A. L. Fradkov, Nonlinear and Adaptive Control of Complex Dynamical Systems (Nauka, St. Petersburg, 2000) [in Russian].MATHGoogle Scholar
  3. 3.
    D. Peaucelle and D. Arzelier, “Robust performance analysis with LMI-based methods for real parametric uncertainty via parameter-dependent Lyapunov functions,” IEEE Trans. Autom. Control 46, 624–630 (2001).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    S. An and W. Liu, “Robust D-stability with mixed-type uncertainties,” IEEE Trans. Autom. Control 49(10), 1878–1884 (2004).MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. L. Corradini, L. Jetto, and G. Orlando, “Robust stabilization of multivariable uncertain plants via switching control,” IEEE Trans. Autom. Control 49, 107–114 (2004).MathSciNetCrossRefGoogle Scholar
  6. 6.
    A. Datta and S. P. Bhattacharyya, “On a quantitative theory of robust adaptive control: An interval plant approach,” IEEE Trans. Autom. Control 41, 570–574 (1996).MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    M. E. Sezer and D. D. Siljak, “On Stability of interval matrices,” IEEE Trans. Autom. Control 39, 368–371 (1994).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    T. A. Akunov and A. V. Ushakov, “Synthesis of systems of guaranteed modal stability,” J. Comput. Syst. Sci. Int. 42, 503–510 (2003).MATHGoogle Scholar
  9. 9.
    V. O. Nikiforov and A. V. Ushakov, Control under Uncertainty: Sensitivity, Adaptation, and Robustness (SPb GITMO, St. Petersburg, 2002) [in Russian].Google Scholar
  10. 10.
    O. V. Slita and A. V. Ushakov, “Providing the invariance of the continuous system output with respect to exogenous signal and endogeneous parametric disturbances: An algebraic approach,” J. Comput. Syst. Sci. Int. 47, 518–526 (2008).MATHCrossRefGoogle Scholar
  11. 11.
    T. A. Akunov, O. V. Slita, and A. V. Ushakov, “Assigning the structure of eigenvectors that makes a dynamical system modally robust with minimum control cost,” Mekhatronika, Avtomatizatsiya, Upravl., No. 2, 6–10 (2008).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • T. A. Akunov
    • 1
  • O. V. Slita
    • 1
  • S. A. Sudarchikov
    • 1
  • A. V. Ushakov
    • 1
  1. 1.St. Petersburg National Research University of Information Technologies, Mechanics, and OpticsSt. PetersburgRussia

Personalised recommendations