Linear Matrix Inequalities for signal processing. An overview
Linear Matrix Inequalities for signal processing. An overview
V. Balakrishnan and L. Vandenberghe
Invited presentation at the 32nd Annual Conference on Information
Sciences and Systems
Department of Electrical Engineering, Princeton University,
Princeton NJ, March 1998
Abstract:
A wide variety of problems in system theory can be
formulated (or reformulated) as convex optimization
problems involving linear matrix inequalities (LMIs), that
is, constraints requiring an affine combination of
symmetric matrices to be positive semidefinite. Important
examples are the analysis of and design for uncertain systems,
and optimal digital filter design and realization. For a
few very special cases, there are ``analytical solutions''
to LMI optimization problems, but in general they can be
solved numerically very efficiently. Thus, the reduction
of a problem from system theory to an optimization problem
based on LMIs constitutes, in a sense, a ``solution'' to
the original problem. Our objective in this paper is to
focus on the application of LMI optimization to problems
from signal processing.
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