Crossover frequency limitations in MIMO nonminimum phase feedback systems

Oded Yaniv*, Per Olof Gutman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This note investigates limitations and design tradeoffs of the closed-loop sensitivity/performance of linear-time-invariant nonminimum-phase uncertain multiple-input-multiple-output plants, with l inputs and m outputs, where m ≤ l. It is shown that if rows i1,..., ik of the plant transfer function form a k × l nonminimum phase transfer matrix, and if the design is such that the sensitivity gain of k - 1 rows among the rows i1,..., ik of the closed-loop transfer function is low, then by necessity the sensitivity gain of the remaining row is high. This sensitivity constraint is quantified with the help of the crossover frequency restriction of a specially constructed single-input-single-output transfer function that includes the right half plane zeros and poles of the k × l transfer matrix.

Original languageEnglish
Pages (from-to)1560-1564
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number9
StatePublished - Sep 2002


  • Feedback control
  • Linear systems
  • Multivariable systems
  • Nonminimum phase
  • Sensitivity


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