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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