Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation

B. Roorda, S. Weiland

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We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is analysed for linear time-invariant finite dimensional systems, in a behavioral l2-setting, without reference to input/output decompositions and stability considerations. The notion of a weakest past-future link is introduced and it is shown how this concept is applied for the purpose of model reduction. A method that reduces the state dimension by one is presented and shown to be optimal. Specific algorithms are provided for the numerical implementation of the approximation method.
Original languageEnglish
Place of PublicationTilburg
Number of pages34
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper


  • Optimal model reduction
  • State space balancing
  • l2-systems
  • Least squares optimization
  • Gap metrics
  • Hankelnorm reduction


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