Name
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<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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.automatica.2011.02.026 | Automatica |
Keywords | Field | DocType |
Stability,Positive polynomials,LMI,Toeplitz matrices | Trigonometric polynomial,Mathematical optimization,Combinatorics,Polynomial matrix,Polynomial,Matrix (mathematics),Positive-definite matrix,Pure mathematics,Toeplitz matrix,Symmetric matrix,Mathematics,Schur polynomial | Journal |
Volume | Issue | ISSN |
47 | 7 | 0005-1098 |
Citations | PageRank | References |
1 | 0.38 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mustapha Ait Rami | 1 | 143 | 10.15 |
| Didier Henrion | 2 | 987 | 88.48 |