• Leonid Fridman
  • Alexander Poznyak
  • Francisco Javier Bejarano
Part of the Systems & Control: Foundations & Applications book series (SCFA)


Robust control is a branch of modern control theory that explicitly deals with uncertainty in its approach to controller design. Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modelling errors. The classical control design, based on the frequency domain methodology, was fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness [1], prompting research to improve them. This was the start of the theory of robust control, which took shape in the 1980s and 1990s and is still active today. In contrast with an adaptive control policy, a robust control policy is static; rather than adapting to measurements of variations, the controller is designed to work assuming that certain variables will be unknown but, for example, bounded [2, 3].


Robust Control Slide Mode Control Slide Mode Controller Nominal Trajectory Initial Time Moment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    M. Athans, Editorial on the lqg problem. IEEE Trans. Autom. Control 16(6), 528 (1971)CrossRefGoogle Scholar
  2. 2.
    J. Ackermann, GermanRobuste Regelung (Springer, New York, 2011)Google Scholar
  3. 3.
    M. Morari, E. Zafiriou, Robust Process Control Theory (Prentice Hall, Englewood Cliffs, 1989)Google Scholar
  4. 4.
    M.G. Safonov, Stability and Robustness of Multivariable Feedback Systems (MIT Press, Cambridge, 1980)MATHGoogle Scholar
  5. 5.
    K. Zhou, J. Doyle, Essentials of Robust Control (Prentice Hall, New Jersey, 1999)Google Scholar
  6. 6.
    D. McFarlane, K. Glover, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Lectures Notes in Control and Information Sciences (Springer, New York, 1989)Google Scholar
  7. 7.
    L. Ray, R. Stengel, Stochastic robustness of linear-time-invariant control systems. IEEE Trans. Automat. Control 36(1), 82–87 (1991)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    S. Bhattacharyya, H. Chapellat, L. Keel, Robust Control: The Parametric Approach (Prentice Hall, New Jersey, 1995)MATHGoogle Scholar
  9. 9.
    V. Boltynaski, A. Poznyak, The Robust Maximum Principle: Theory and Applications (Birkhauser, New York, 2012)CrossRefGoogle Scholar
  10. 10.
    V. Utkin, First stage of vss: people and events, in Variable Structure Systems: Towards the 21st Century, ed. by X. Yu, J.-X. Xu. Lectures Notes in Control and Information Sciences, vol. 274 (Springer, London, 2002), pp. 1–32Google Scholar
  11. 11.
    V. Utkin, Sliding Modes in Control and Optimization (Springer, Berlin, 1992)CrossRefMATHGoogle Scholar
  12. 12.
    C. Edwards, S.K. Spurgeon, Sliding Mode Control: Theory and Applications (CRC Press, New York, 1998)Google Scholar
  13. 14.
    Y. Shtessel, C. Edwards, L. Fridman, A. Levant, Sliding Mode Control and Observation (Birkhäuser, Boston, 2013)Google Scholar
  14. 15.
    A. Filippov, Differential Equations with Discontinuous Right-hand Sides (Kluwer, Dordrecht, 1988)CrossRefMATHGoogle Scholar
  15. 16.
    B. Drazenovic, The invariance conditions in variable structure systems. Automatica 5, 287–295 (1969)CrossRefMATHMathSciNetGoogle Scholar
  16. 17.
    A. Lukyanov, V. Utkin, Methods of reducing equations for dynamic systems to a regular form. Autom. Rem. Control 42(4), 413–420 (1981)MathSciNetGoogle Scholar
  17. 18.
    X.-G. Yan, S. Spurgeon, C. Edwards, Dynamic sliding mode control for a class of systems with mismatched uncertainty. Eur. J. Control 11, 1–10 (2005)CrossRefMathSciNetGoogle Scholar
  18. 19.
    H. Choi, An lmi-based switching surface design method for a class of mismatched uncertain systems. IEEE Trans. Autom. Control 48(9), 1634–1638 (2003)CrossRefGoogle Scholar
  19. 20.
    A. Estrada, L. Fridman, Quasi-continuous hosm control for systems with unmatched perturbations. Automatica 11, 1916–1919 (2010)CrossRefMathSciNetGoogle Scholar
  20. 21.
    A. Estrada, L. Fridman, Integral hosm semiglobal controller for finite-time exact compensation of unmatched perturbations. IEEE Trans. Autom. Control 55(11), 2644–2649 (2010)CrossRefMathSciNetGoogle Scholar
  21. 22.
    A. Poznyak, Y. Shtessel, C. Gallegos, Mini-max sliding mode control for multi-model linear time varying systems. IEEE Trans. Autom. Control 48(12), 2141–2150 (2003)CrossRefGoogle Scholar
  22. 23.
    G. Herrmann, S. Spurgeon, C. Edwards, A model-based sliding mode control methodology applied to the hda plant. J. Process Control 13, 129–138 (2003)CrossRefGoogle Scholar
  23. 24.
    F. Castaños, L. Fridman, Dynamic switching surfaces for output sliding mode control: an h approach. Automatica 47(7), 1957–1961 (2011)CrossRefMATHGoogle Scholar
  24. 25.
    A. Ferreira, F. Bejarano, L. Fridman, Unmatched uncertainties compensation based on high-order sliding mode observation. Int. J. Robust Nonlinear Control 23(7), 754–764 (2013)CrossRefMATHGoogle Scholar
  25. 26.
    G.P. Matthews, R.A. DeCarlo, Decentralized tracking for a class of interconnected nonlinear systems using variable structure control. Automatica 24, 187–193 (1988)CrossRefMATHMathSciNetGoogle Scholar
  26. 27.
    V.I. Utkin, J. Shi, Integral sliding mode in systems operating under uncertainty conditions, in Proceedings of the 35th IEEE-CDC, Kobe, Japan, 1996Google Scholar
  27. 28.
    F. Castaños, L. Fridman, Analysis and design of integral sliding manifolds for systems with unmatched perturbations. IEEE Trans. Autom. Control 55(5), 853–858 (2006)CrossRefGoogle Scholar
  28. 29.
    M. Rubagotti, A. Estrada, F. Castaños, A. Ferrara, L. Fridman, Integral sliding mode control for nonlinear systems with matched and unmatched perturbations. IEEE Trans. Autom. Control 56(11), 2699–2704 (2011)CrossRefGoogle Scholar
  29. 30.
    J.-X. Xu, W. Cao, Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems. Proc. Am. Control Conf. 6, 4369–4374 (2001)CrossRefGoogle Scholar
  30. 32.
    F. Castaños, J. Xu, L. Fridman, Integral sliding modes for systems with matched and unmatched uncertainties. Advances in Variable Structure and Sliding Mode Control. Lecture Notes in Control and Information Sciences, vol. 334 (Springer, Berlin, 2006), pp. 227–246Google Scholar
  31. 33.
    F. Bejarano, L. Fridman, A. Poznyak, Output integral sliding mode control based on algebraic hierarchical observer. Int. J. Control 80(3), 443–453 (2007)CrossRefMATHMathSciNetGoogle Scholar
  32. 34.
    F.J. Bejarano, L.M. Fridman, A.S. Poznyak, Output integral sliding mode for min–max optimization of multi-plant linear uncertain systems. IEEE Trans. Autom. Control 54(11), 2611–2620 (2009)CrossRefMathSciNetGoogle Scholar
  33. 35.
    B. Anderson, J. Moore, Optimal Control: Linear Quadratic Methods. Information and Systems Science (Prentice Hall, London, 1990)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Leonid Fridman
    • 1
  • Alexander Poznyak
    • 2
  • Francisco Javier Bejarano
    • 3
  1. 1.Departamento de Ingeniería de Control y RobóticaUniversidad Nacional Autonoma de MexicoMexico CityMexico
  2. 2.Department of Control AutomaticoCentro de Investigacion y Estudios Avanzados (CINVESTAV)Mexico CityMexico
  3. 3.Department of Research and Posgraduates Studies (SEPI)ESIME Ticomán, Instituto Politécnico NacionalMexico CityMexico

Personalised recommendations