Infinitesimal Characterizations for Strong Invariance and Monotonicity for Non-Lipschitz Control Systems
Abstract
We provide new infinitesimal characterizations for strong invariance of multifunctions in terms of Hamiltonian inequalities and tangent cones. In lieu of the standard local Lipschitzness assumption on the multifunction, we assume a new feedback realizability condition that can in particular be satisfied by control systems that are discontinuous in the state variable. Our realization condition is based on H. Sussmann's unique limiting property, and allows a more general class of feedback realizations than is allowed by the recent strong invariance characterizations of Krastanov, Malisoff, and Wolenski. We also give new nonsmooth monotonicity characterizations for control systems that may be discontinuous in the state.
Cite
@article{arxiv.math/0405586,
title = {Infinitesimal Characterizations for Strong Invariance and Monotonicity for Non-Lipschitz Control Systems},
author = {Michael Malisoff},
journal= {arXiv preprint arXiv:math/0405586},
year = {2007}
}
Comments
19 pages, 0 figures. For this revision, the author added a remark about an alternative nonconstructive proof of the main result