Semidefinite programming duality and
linear system theory: connections and implications for
computation
Semidefinite programming duality and
linear system theory: connections and implications for
computation
L. Vandenberghe and V. Balakrishnan
In Proc. IEEE Conference on Decision and Control,
pages 989-994, Phoenix, Arizona, December 1999
Abstract:
Several important problems in control theory can be
reformulated as semidefinite programming problems (SDPs), \ie,
as convex optimization problems with linear matrix inequality
(LMI) constraints. From duality theory in convex optimization,
dual problems can be derived for these SDPs.
These dual problems 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. Specifically, we discuss
the following three applications of SDP duality.
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