Convex delay endomorphisms

Dynamics of Vertical Delay Endomorphisms

Blaschke- and Minkowski-endomorphisms of Convex Bodies

We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...

The Endomorphisms of the Lattice of Closed Convex Cones

The set of closed convex cones in R (d ≥ 3), with the operations of intersection and closed sum, is a lattice. We determine all endomorphisms of this lattice. As a consequence, we obtain a characterization of the duality of convex cones. MSC 2000: 52A20

Risk, Delay, and Convex Self-Control Costs

The dual-self model supposes that decision-making involves a conflict between the desire for immediate and safe gratification on the one hand, and riskier long term benefits on the other. This conflict is resolved through a decision criterion that puts weights on both desires. A key element of the model is that this weighting is endogenous, and that changes in constraints that have the same eff...

Delay-dependent reciprocally convex combination lemma

This paper deals with the stability analysis of linear systems subject to fast-varying delays. The main result of this paper is the derivation of a delay-dependent reciprocally convex lemma allowing a notable reduction of the conservatism of the resulting stability conditions at the reasonable price of additional decision variables. Several examples are studied to show the potential of the prop...