Title :
On the rank minimization problem over a positive semidefinite linear matrix inequality
Author :
Mesbahi, M. ; Papavassilopoulos, G.P.
Author_Institution :
Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA
fDate :
2/1/1997 12:00:00 AM
Abstract :
We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite. Our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice. This problem is of importance in many contexts, for example in feedback synthesis problems, and such an example is also provided
Keywords :
control system synthesis; eigenvalues and eigenfunctions; feedback; matrix algebra; minimisation; MIN RANK problem; eigenvalues; least element theory; linear matrix inequality; ordered linear complementarity; output feedback synthesis; positive semidefinite matrix; rank minimization; vector lattice; Control theory; Eigenvalues and eigenfunctions; Feedback; Lattices; Linear matrix inequalities; Linear programming; Mechanical factors; Propulsion; Symmetric matrices; Vectors;
Journal_Title :
Automatic Control, IEEE Transactions on
