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Article Dans Une Revue Automatica Année : 2011

A hierarchy of LMI inner approximations of the set of stable polynomials}

Résumé

Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) 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 $n < m$. It is shown that when $m$ tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in $n$) already studied in the technical literature.
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Dates et versions

hal-00496527 , version 1 (30-06-2010)

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Mustapha Ait Rami, Didier Henrion. A hierarchy of LMI inner approximations of the set of stable polynomials}. Automatica, 2011, 47 (7), pp.1455-1460. ⟨hal-00496527⟩
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