Representation of Linear Sets as Critical Sets

2 Linear Matrix Inequality Representation of Sets

2 Linear Matrix Inequality Representation of Sets

This article concerns the question: which subsets of R 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 re...

Critical sets of proper

A characterization of critical sets and their images for suitable proper Whitney functions in the plane is given. More precisely, necessary and suucient conditions are provided for the existence of proper Whitney extensions F of f : C ! R 2 such that C is the critical set of F. This result relies strongly on theorems of Blank and Troyer.

U−Sets as probabilistic sets

Using topos theory I prove that reasoning about probabilities can be formalized with only one simple assumption: given two sets of measures A,B, if B ⊆ A, then B is less imprecise than A.

LK-INTERIOR SYSTEMS AS SYSTEMS OF “ALMOST OPEN” L-SETS

We study interior operators and interior structures in a fuzzy setting.We investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.