TY - GEN

T1 - Lipschitz selections of convexifications of pseudo-lipschitz multifunctions and the Lipschitz maximum principle for differential inclusions

AU - Sussmann, Héctor J.

PY - 2010

Y1 - 2010

N2 - We prove that, if X, Y are finite-dimensional real linear spaces and F : X → 2Y is a multifunction that has the pseudo-Lipschitz property at a point (x0, y0) 2 Graph(F), then for every ε > 0 there exists a Lipschitz multifunction Vε : N(ε) → 2Y, defined on a neighborhood N(ε) of x0, such that (i) Vε has compact convex values, (ii) Vε(x 0) = {y0}, and (iii) for every x ∈ N(ε), V ε(x) is a subset of the convex hull co(Fε(x)) of the intersection Fε(x) of F(x) with the closed ε-ball centered at y0. In particular, this implies the existence of a Lipschitz single-valued selection fε of co(Fε) near x 0 satisfying fε(x0) = y0.

AB - We prove that, if X, Y are finite-dimensional real linear spaces and F : X → 2Y is a multifunction that has the pseudo-Lipschitz property at a point (x0, y0) 2 Graph(F), then for every ε > 0 there exists a Lipschitz multifunction Vε : N(ε) → 2Y, defined on a neighborhood N(ε) of x0, such that (i) Vε has compact convex values, (ii) Vε(x 0) = {y0}, and (iii) for every x ∈ N(ε), V ε(x) is a subset of the convex hull co(Fε(x)) of the intersection Fε(x) of F(x) with the closed ε-ball centered at y0. In particular, this implies the existence of a Lipschitz single-valued selection fε of co(Fε) near x 0 satisfying fε(x0) = y0.

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U2 - 10.1109/CDC.2010.5718096

DO - 10.1109/CDC.2010.5718096

M3 - Conference contribution

AN - SCOPUS:79953129121

SN - 9781424477456

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3403

EP - 3408

BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 49th IEEE Conference on Decision and Control, CDC 2010

Y2 - 15 December 2010 through 17 December 2010

ER -