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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