Min-Max Sliding-Mode Control

  • Vladimir G. Boltyanski
  • Alexander S. Poznyak
Part of the Systems & Control: Foundations & Applications book series (SCFA)


This chapter deals with the Min-Max Sliding-Mode Control design where the original linear time-varying system with unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances. Such a trade-off between an original uncertain linear time-varying dynamic system and a corresponding higher order multimodel system with complete knowledge leads to a linear multimodel system with known bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed Min-Max Sliding-Mode Control strategy gives an optimal robust sliding-surface design algorithm, which is reduced to a solution of the equivalent LQ Problem that corresponds to the weighted performance indices with weights from a finite-dimensional simplex. An illustrative numerical example is presented.


Uncertain Case Bounded Disturbance Quadratic Performance Index Exact Realization Unknown Bounded Disturbance 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vladimir G. Boltyanski
    • 1
  • Alexander S. Poznyak
    • 2
  1. 1.CIMATGuanajuatoMexico
  2. 2.Automatic Control DepartmentCINVESTAV-IPNMéxicoMexico

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