Integral Sliding Mode Control

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


In this chapter the concept of integral sliding mode (ISM) is revisited. The efficiency of ISM is illustrated on the example of LQ control. Then the projection to the unmatched variable subspace is designed ensuring that the application of ISM is not amplifying, but minimizing the unmatched perturbations. An illustrative example of application of ISM to LQ problem is presented.


Slide Mode Control Linear Quadratic Regulator Equivalent Control Nominal Control Integral Slide Mode Control 
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  1. 13.
    V. Utkin, J. Guldner, J. Shi, Sliding Mode Control in Electromechanical Systems (Taylor & Francis Inc., Philadelphia, 1999)Google Scholar
  2. 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
  3. 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
  4. 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
  5. 35.
    B. Anderson, J. Moore, Optimal Control: Linear Quadratic Methods. Information and Systems Science (Prentice Hall, London, 1990)MATHGoogle Scholar
  6. 36.
    A. Isidori, Nonlinear Control Systems, 3rd edn. Communications and Control Engineering (Springer, New York, 1995)CrossRefMATHGoogle Scholar
  7. 37.
    L. Fridman, F. Castaños, N. M’Sirdi, N. Khraef, Decomposition and robustness properties of integral sliding mode controllers, in 8th International Workshop on Variable Structure Systems, Spain, Sept 2004, paper no. f-30Google Scholar
  8. 40.
    J.-X. Xu, Y. Pan, T. Lee, Analysis and design of integral sliding mode control based on Lyapunov’s direct method. in Proceedings of the American Control Conference, Denver, Colorado, June 2003, pp. 192–196Google 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

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