Robust
Stability and Performance Analysis of Uncertain Systems Using Linear Matrix
Inequalities
Robust
Stability and Performance Analysis of Uncertain Systems Using Linear Matrix
Inequalities
V. Balakrishnan and R. L. Kashyap.
In Journal of Optimization Theory and Applications, vol. 100, no. 3,
pages 457-478, March 1999
Abstract:
A wide variety of problems in system and control 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. For a few
very special cases, there are ``analytical solutions'' to
these problems, but in general they can be solved
numerically very efficiently. Thus, the reduction of a
control problem to an optimization problem based on LMIs
constitutes, in a sense, a ``solution'' to the original
problem. The objective of this article is to provide a
tutorial on the application of optimization based on LMIs
to robust control problems. In the first part of the
article, we provide a brief introduction to optimization
based on LMIs. In the second part, we describe a specific
example, that of robust stability and performance analysis
of uncertain systems using LMI optimization.
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