Variable structure controller design for linear systems with bounded inputs

  • Shengjian Bai
  • Pinhas Ben-TzviEmail author
  • Qingkun Zhou
  • Xinsheng Huang
Regular Papers Control Theory


This paper studies the design of variable structure systems with saturation inputs. Sliding mode domain, reaching domain, and unescapable reaching domain of linear systems with variable structure are defined and investigated. When the state matrix of the linear system is Hurwitz, the stability of the variable structure systems is proven by using passivity theory. Moreover, variable structure systems with novel nonlinear switching surfaces are proposed for second order systems. Two strategies for designing variable structure control for high order linear systems are also proposed, such as stepby-step variable structure control and moving-surface variable structure control, which were found to guarantee that the reaching condition of the variable structure control is always satisfied. Finally, an illustrative example pertaining to the attitude control of a flexible spacecraft demonstrates the effectiveness of the proposed methods.


Bounded inputs linear systems nonlinear switching surface passivity theory variable structure control 


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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shengjian Bai
    • 1
  • Pinhas Ben-Tzvi
    • 2
    Email author
  • Qingkun Zhou
    • 1
  • Xinsheng Huang
    • 1
  1. 1.College of Mechatronics Engineering and AutomationNational University of Defense TechnologyChangsha, HunanP. R. China
  2. 2.Robotics and Mechatronics Laboratory, School of Engineering and Applied ScienceThe George Washington UniversityWashington, DCUSA

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