An alternate geometric perspective on MIMO systems

M. L. Nagurka, T. R. Kurfess

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


An alternate graphical representation of linear, time-invariant, multi-input, multi-output (MIMO) system dynamics is proposed that is highly suited for exploring the influence of closedloop system parameters. The development is based on the adjustment of a scalar forward gain multiplying a cascaded multivariable controller/plant embedded in an output feedback configuration. By tracking the closed-loop eigenvalues as explicit functions of gain, it is possible to visualize the multivariable root loci in a set of “gain plots” consisting of two graphs: (i) magnitude of system eigenvalues versus gain and (ii) argument (angle) of system eigenvalues versus gain. The gain plots offer an alternative perspective of the standard MIMO root locus plot by depicting unambiguously the polar coordinates of each eigenvalue in the complex plane. Two example problems demonstrate the utility of gain plots for interpreting closed-loop multivariable system behavior.

Original languageEnglish
Pages (from-to)538-543
Number of pages6
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Issue number3
StatePublished - 1 Jan 1993
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications


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