Brief paper: A hierarchy of LMI inner approximations of the set of stable polynomials

  • Authors:

  • Mustapha Ait Rami;Didier Henrion

  • Affiliations:

  • Departamento de Ingenierí/a de Sistemas y Automá/tica, Facultad de Ciencias, Universidad de Valladolid, calle Real de Burgos s/n, SP-47011 Valladolid, Spain;CNRS/ LAAS/ 7 avenue du colonel Roche, F-31077 Toulouse, France and Université/ de Toulouse/ UPS, INSA, INP, ISAE/ LAAS/ F-31077 Toulouse, France and Faculty of Electrical Engineering, Czech T ...

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for the positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMIs) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size m) of the nonconvex set of Schur stable polynomials of given degree n