Rank-one LMIs and Lyapunov's inequality

Authors
Henrion, D Meinsma, G
Citation
D. Henrion et G. Meinsma, Rank-one LMIs and Lyapunov's inequality, IEEE AUTO C, 46(8), 2001, pp. 1285-1288
Citations number
12
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN journal
00189286 → ACNP
Volume
46
Issue
8
Year of publication
2001
Pages
1285 - 1288
Database
ISI
SICI code
0018-9286(200108)46:8<1285:RLALI>2.0.ZU;2-K
Abstract
We describe a new proof of the well-known Lyapunov's matrix inequality abou t the location of the eigenvalues of a matrix in some region of the complex plane. The proof makes use of standard facts from quadratic and semidefini te programming. Links are established between the Lyapunov matrix, rank-one linear matrix inequalities (LMIs), and the Lagrange multiplier arising in duality theory.