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Optimal induced norm computation of discrete H ∞ control systems with time-delays

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Abstract

Time-delays in state or control can never be eliminated in many discrete systems, like computer controlled systems. Introducing an extended state vector, the original equations with time-delays can be transformed into standard equations without time-delays. Then the theory and methods of usual discrete system can be applied. Based on analogies between structural mechanics and optimal control theory, the optimal norm corresponding to the fundamental frequency of structural vibration, which is a Rayleigh-quotient problem, can be solved by extended Wittrick–Williams algorithm. Numerical results disclose that the optimal norm does not increase monotonously with time-delays and can be decreased effectively by selecting appropriate time delays.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116023, China

    Shujun Tan, Zhigang Wu & Wanxie Zhong

Authors
  1. Shujun Tan
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  2. Zhigang Wu
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  3. Wanxie Zhong
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Correspondence to Shujun Tan.

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Tan, S., Wu, Z. & Zhong, W. Optimal induced norm computation of discrete H ∞ control systems with time-delays. J Glob Optim 40, 653–662 (2008). https://doi.org/10.1007/s10898-006-9118-9

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  • DOI: https://doi.org/10.1007/s10898-006-9118-9

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