Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
Relaxation Methods of Parametrized LMIs Based on D.C. and Multiconvex Technique
Hiroyuki ICHIHARAEitaku NOBUYAMATakanori ISHII
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2003 Volume 16 Issue 12 Pages 649-654

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Abstract

This paper gives relaxation methods reducing a feasibility or optimization problem under a parametrized linear matrix inequality constraint to a finite number of LMIs constraint. The methods are based on convexification of difference of convex (d.c.) and multiconvexification. We propose a generalized relaxation method of d.c. convexification and a unified relaxation method between d.c convexification and multiconvexification techniques. These methods are applied to stability analysis and L2 gain analysis of parameter-dependent systems. Numerical examples are illustrated for each applications.

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