Semidefinite Programming Duality and
Linear Time-invariant Systems
Semidefinite Programming Duality and
Linear Time-invariant Systems
V. Balakrishnan
Presented at the Department of Mechanical Engineering, University
of Houston, February 2003
and
the Hamilton Institute, May 2003
Abstract
Several important problems in systems and 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 present such connections for a few problems associated with
linear time-invariant systems.
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