Single-loop feedback-stabilization of linear multivariable dynamical plants

  • Authors:

  • D. C. Youla;J. J. Bongiorno, Jr.;C. N. Lu

  • Affiliations:

  • -;-;-

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1974

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Abstract

This paper derives the necessary and sufficient conditions for a multivariable plant P(s) with asymptotically stable hidden modes to be stabilizable by means of singleloop feedback employing an asymptotically stable controller and feedback sensor. These conditions are completely general and therefore encompass unstable, nonminimum-phase plants as well. For single-input-output plants with zero gain at infinite frequency the conditions reduce to the sole requirement that no plant zeros on the nonnegative real axis of the complex s-plane lie to the left of an odd number of real plant poles, multiple poles counted according to their multiplicities. It has also been possible to derive simple necessary and sufficient conditions for a closed-loop transfer function T(s) to be realizable by asymptotically stable compensation around a prescribed single-input-output plant P(s). It is expected that this latter result can be suitably generalized to the multivariable case. In a real sense, this paper constitutes a continuation of some earlier unpublished work [8] by the first author.