Strictly positive real admittances for coupled stability

J. Edward Colgate*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This paper builds upon recent work that has addressed the stability of a feedback- controlled robot coupled to a passive, dynamic environment. A new definition of a "strictly positive real" function is presented, and is used to provide necessary and sufficient conditions for the exponential stability of a coupled system comprising a 1-port robot with a strictly positive real admittance, and a 1-port environment with a positive real (but otherwise arbitrary) impedance. The distinction between the new definition and conventional definitions of a strictly positive real function is founded in physical systems theory; the new definition relies upon distinct roles for efforts and flows, and upon the concept of an excess state. This definition will provide a useful design constraint for the development of robust robot controllers.

Original languageEnglish (US)
Pages (from-to)429-444
Number of pages16
JournalJournal of the Franklin Institute
Issue number3
StatePublished - May 1992
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics


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