Title :
Rank-one LMIs and Lyapunov´s inequality
Author :
Henrion, Didier ; Meinsma, Gjerrit
Author_Institution :
Lab. d´´Analyse et d´´Archit. des Syst., CNRS, Toulouse, France
Abstract :
We describe a new proof of the well-known Lyapunov´s matrix inequality about 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 semi-definite programming. Links are established between the Lyapunov matrix, rank-one LMI and the Lagrange multiplier arising in duality theory
Keywords :
Lyapunov matrix equations; duality (mathematics); eigenvalues and eigenfunctions; quadratic programming; Lagrange multiplier; Lyapunov matrix; Lyapunov matrix inequality; complex plane; duality theory; matrix eigenvalues; quadratic programming; rank-one LMI; semi-definite programming; Conformal mapping; Eigenvalues and eigenfunctions; Lagrangian functions; Linear matrix inequalities; Linear programming; Marine vehicles; Mathematics; Quadratic programming; Stability; Virtual colonoscopy;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.912068
