Variable structure control for sampled-data systems

  • Katsuhisa Furuta
  • Yaodong Pan
Part B Hybrid Systems
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 241)


For a continuous-time system, a sliding sector is designed as a subset of the system state space, where some norm of the state decreases. The continuous-time VS control law is designed to move the system state from the outside to the inside of the sliding sector. The sector is defined as the PR-Sliding Sector where the norm is defined as the quadratic form of the state with the symmetric matrix P and its derivative is less than negative of a quadratic form of the state with the matrix R. In the paper, the discrete-time VS controller for the sampled-data system is designed as an extension of the continuous-time VS controller. The discrete-time sliding sector is to be defined as a subset of the continuous-time sliding sector. The discrete-time VS control law is equal to the continuous-time VS control law at every sampling instant. It is proved that such discrete-time sliding sector for a sampled-data system exists and the proposed discrete-time VS controller quadratically stabilizes the sampled-data system if the sampling interval and the feedback coefficient are chosen suitably. Simulation result is given to show the effectiveness of the proposed VS controller for sampled-data systems.


Riccati Equation Sampling Instant Positive Definite Symmetric Matrix Variable Structure Control Pendulum System 
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Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Katsuhisa Furuta
  • Yaodong Pan
    • 1
  1. 1.Department of Mechanical and Environmental InformaticsTokyo Institute of TechnologyTokyoJapan

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