An Algebraic Formula for Performance Bounds of a Weighted H∞ Optimal Control Problem

Andres A. Peters, Francisco J. Vargas, Jie Chen

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This article provides performance bounds for a particular \mathcal {H}-\infty model-matching problem. We consider scalar linear time-invariant plants in a one-degree-of-freedom control loop. We obtained explicit expressions for the Gramians needed when Nehari's theorem is applied to this problem, leading to a simple algebraic equation for the optimal performance. This formula sheds light upon the effect that nonminimum-phase zeros have on the optimal performance and yields easily computable bounds and approximations.

Original languageEnglish
Article number9042269
Pages (from-to)781-786
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2021


  • Discrete-Time systems
  • control
  • performance bounds

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