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AUTOMATICA
2011

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

7 years 10 months ago
A hierarchy of LMI inner approximations of the set of stable polynomials
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. An application to robust controller design is described.
Mustapha Ait Rami, Didier Henrion
Added 24 Aug 2011
Updated 24 Aug 2011
Type Journal
Year 2011
Where AUTOMATICA
Authors Mustapha Ait Rami, Didier Henrion
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