Title :
Rank-one LMIs and Lyapunov´s inequality
Author :
Henrion, Didier ; Meinsma, Gjerrit
Author_Institution :
Lab. d´´Autom. et d´´Anal. des Syst., CNRS, Toulouse, France
fDate :
8/1/2001 12:00:00 AM
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 semidefinite programming. Links are established between the Lyapunov matrix, rank-one linear matrix inequalities (LMI), and the Lagrange multiplier arising in duality theory
Keywords :
Lyapunov matrix equations; duality (mathematics); eigenvalues and eigenfunctions; quadratic programming; Lagrange multiplier; Lyapunov matrix inequality; duality theory; matrix eigenvalues; quadratic programming; rank-one LMI; rank-one linear matrix inequalities; semidefinite programming; Automation; Conformal mapping; Eigenvalues and eigenfunctions; Information theory; Lagrangian functions; Linear matrix inequalities; Linear systems; Mathematics; Quadratic programming; Stability;
Journal_Title :
Automatic Control, IEEE Transactions on
