Sliding Modes for Switched Uncertain Linear Time Invariant Systems: An Output Integral Sliding Mode Approach

  • Leonid Fridman
  • Rosalba Galván-GuerraEmail author
  • Juan-Eduardo Velázquez-Velázquez
  • Rafael Iriarte


A robustifying methodology for switched uncertain linear time invariant systems with matched uncertainties/perturbations and state-dependent location transitions using only output information is presented. An output integral sliding mode control technique, based on an algebraic hierarchical observer is proposed. This approach allows the theoretically exact compensation of the matched uncertainties/perturbations right after the initial time; but it requires the use of filters to reconstruct the state vector and produces a high level of chattering. To eliminate the necessity of filtering and to diminish the chattering, a continuous output integral sliding mode controller is designed. This controller is based on the super-twisting algorithm and it compensates the matched uncertainties/perturbations after a finite transient. For this case, sufficient conditions to ensure the convergence of the controller and the observer before every switching are given. The proposed approach is illustrated via numerical simulations.



My co-authors and myself are happy to prepare this chapter for this book reflecting some new results developing the concept of output integral sliding mode that we proposed with you, Professor Alexander Poznyak, 10 years ago. Thank you for your creativity, kindness, and constant support. Happy birthday and long life.

Leonid Fridman would like to acknowledge the financial support of the project 113216 of PAPIIT-UNAM.

Leonid Fridman


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Leonid Fridman
    • 1
  • Rosalba Galván-Guerra
    • 2
    Email author
  • Juan-Eduardo Velázquez-Velázquez
    • 2
  • Rafael Iriarte
    • 1
  1. 1.Facultad de IngenieríaUniversidad Nacional Autonoma de MéxicoMexico CityMexico
  2. 2.Unidad Profesional Interdisciplinaria de Ingeniería Campus HidalgoInstituto Politécnico NacionalHidalgoMexico

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