"6"^^ . . "RIV/68407700:21230/11:00180622" . "183839" . "1"^^ . . . "2"^^ . "21230" . "4" . "Henrion, Didier" . "A hierarchy of LMI inner approximations of the set of stable polynomials"@en . . "Ait Rami, M." . "A hierarchy of LMI inner approximations of the set of stable polynomials"@en . "A hierarchy of LMI inner approximations of the set of stable polynomials" . "Automatica" . . . . . . "10.1016/j.automatica.2011.02.026" . "0005-1098" . . "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 sizem) 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."@en . . "[54CF01E9CEF6]" . "000292074400019" . . . "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 sizem) 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." . "P(GAP103/10/0628)" . . "A hierarchy of LMI inner approximations of the set of stable polynomials" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "Stability; Positive polynomials; LMI; Toeplitz matrices"@en . "RIV/68407700:21230/11:00180622!RIV12-GA0-21230___" . "47" . . . "Henrion, Didier" .