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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

1 Scopus Citations
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  • Andres A. Peters
  • Francisco Vargas
  • Jie Chen

Related Research Unit(s)


Original languageEnglish
Article number9042269
Pages (from-to)781-786
Number of pages6
Journal / PublicationIEEE Transactions on Automatic Control
Issue number2
Online published19 Mar 2020
Publication statusPublished - Feb 2021


This note provides performance bounds for a particular H model matching problem. We consider scalar linear time invariant (LTI) plants in an 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 non-minimum phase zeros have on the optimal performance, and yields easily computable bounds and approximations.

Research Area(s)

  • H∞ control, Discrete-time systems, Performance bounds