Brief Pole structure assignment via non-regular static state feedback

  • Authors:
  • J. J. Loiseau;P. Zagalak;V. Kuera

  • Affiliations:
  • Institut de Recherche en Cybernétique de Nantes, UMR 6597 CNRS, Ecole Centrale de Nantes, BP 92101, F-44321, Nantes Cedex 03, France;Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, P.O. Box 18, 18208 Praha, Czech Republic;Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, P.O. Box 18, 18208 Praha, Czech Republic and Trnka Laboratory for Automatic Control, Faculty of Electrica ...

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1999

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Abstract

The limits of the static state feedback u=Fx+Gv, with G not necessarily nonsingular, in altering the transmission pole structure of the linear system x@?=Ax+Bu are studied. A necessary and sufficient condition for a list of polynomials to be the denominator polynomials of the Smith-McMillan form of the closed-loop transfer matrix (sI-A-BF)^-^1BG is established. The condition involves the calculation of the infimal set of the controllability indices that the system can attain through feedback while satisfying the Rosenbrock inequalities.