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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Veröffentlicht in:	IEEE transactions on automatic control Jg. 48; H. 1; S. 30 - 41
Hauptverfasser:	Balakrishnan, V., Vandenberghe, L.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.01.2003 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	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
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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.
AbstractList	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. 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. (Author)
Author	Balakrishnan, V. Vandenberghe, L.
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SubjectTerms	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
Title	Semidefinite programming duality and linear time-invariant systems
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