Semidefinite programming duality and linear time-invariant systems

Author

Balakrishnan, Venkataramanan ; Vandenberghe, Lieven

Author_Institution

Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN, USA

Volume

48

Issue

1

fYear

2003

fDate

1/1/2003 12:00:00 AM

Firstpage

30

Lastpage

41

Abstract

Several important problems in control theory can be reformulated as semidefinite programming problems, i.e., minimization of a linear objective subject to linear matrix inequality (LMI) constraints. From convex optimization duality theory, conditions for infeasibility of the LMIs, as well as dual optimization problems, can be formulated. These can in turn be reinterpreted in control or system theoretic terms, often yielding new results or new proofs for existing results from control theory. We explore such connections for a few problems associated with linear time-invariant systems.

Keywords

convex programming; eigenvalues and eigenfunctions; linear matrix inequalities; linear systems; time-varying systems; convex optimization duality; dual optimization problems; linear matrix inequality constraints; linear time-invariant systems; semidefinite programming duality; system theoretic terms; Application software; Constraint theory; Control system synthesis; Control systems; Control theory; Controllability; Linear matrix inequalities; Linear programming; Qualifications; Riccati equations;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2002.806652

Filename

1166522