Semidefinite programming duality and linear time-invariant systems

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 op...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 48; no. 1; pp. 30 - 41
Main Authors: Balakrishnan, V., Vandenberghe, L.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2003
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Application software
Applied sciences
Automatic control
Computer science; control theory; systems
Constraint theory
Control system analysis
Control system synthesis
Control systems
Control theory
Control theory. Systems
Controllability
Exact sciences and technology
Joints
Linear matrix inequalities
Linear programming
Minimization
Optimization
Programming
Qualifications
Riccati equations
System theory
Invariant
Linear system
Inequality constraint
Linear matrix inequality
Minimization
Linear programming
Semi definite programming
Linear time
Duality
Invarying system
Convex programming
Constrained optimization
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2002.806652