Linear Matrix Inequality Representation of Sets

Details Linear Matrix Inequality Representation of Sets Linear Matrix Inequality Representation of Sets

2003-06-11

arxiv.org/abs/math/0306180v1

Mathematics

Optimization and Control

Scientific paper

This article concerns the question: which subsets of ${\mathbb R}^m$ can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems as LMIs by automatic methods one needs a good idea of which problems can and cannot be represented by LMIs. Little is currently known about such problems. In this article we give a necessary condition, we call "rigid convexity", which must hold for a set ${\cC} \in {\mathbb R}^m$ in order for ${\cC}$ to have an LMI representation. Rigid convexity is proved to be necessary and sufficient when $m=2$. This settles a question formally stated by Pablo Parrilo and Berndt Sturmfels in [PSprep].

Affiliated with

Also associated with

No associations

Rating

Linear Matrix Inequality Representation of Sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Linear Matrix Inequality Representation of Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear Matrix Inequality Representation of Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-458592