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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