Multiplier Theory and Operator Square Roots: Application to Robust and Time-Varying Stability

  • Brian D. O. Anderson
  • Soura Dasgupta
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 121)


This paper considers the extension of a number of passive multiplier theory based results, previously known only for linear time invariant scalar systems, to time varying and multivariable settings. The extensions obtained here have important applications to the stability of both adaptive systems and linear systems in general. We demonstrate in this paper that at the heart of the extensions carried out here lies the result that if a stable multivariable and/or linear time varying system is stable under all scalar constant, positive feedback gains, then it has a well defined square root. The existence of this square root is demonstrated through a constructive Newton-Raphson based algorithm. The extensions provided here (dealing with robust stability and introduction of time-varying gains) though different in form from their linear time invariant scalar counterparts, do recover these as a special case.


Linear Time Invariant System Single Input Single Output Linear Time Invariant Matrix Transfer Function Linear Time Vary System 
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Copyright information

© Birkhäuser Verlag Basel 1996

Authors and Affiliations

  • Brian D. O. Anderson
    • 1
  • Soura Dasgupta
    • 2
  1. 1.Research School of Information Sciences and EngineeringAustralian National UniversityAustralia
  2. 2.Department of Electrical and Computer EngineeringThe University of IowaIowa CityUSA

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