Semidefinite programming duality and Linear Time-Invariant
systems
Semidefinite programming duality and Linear Time-Invariant
systems
V. Balakrishnan and L. Vandenberghe
Technical Report TR-ECE 02-02, School of Electrical and Computer Engineering,
Purdue University, June 2002
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 re-interpreted 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.
An abridged journal version of the paper can be found
here.
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