Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in $H_\infty$ control
Optimization and Control
2007-05-23 v1
Abstract
This paper deals with the regularity of solutions of the Hamilton-Jacobi Inequality which arises in H-infinity control. It shows by explicit counterexamples that there are gaps between existence of continuous and locally Lipschitz (positive definite and proper) solutions, and between Lipschitz and continuously differentiable ones. On the other hand, it is shown that it is always possible to smooth-out solutions, provided that an infinitesimal increase in gain is allowed.
Cite
@article{arxiv.math/9912007,
title = {Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in $H_\infty$ control},
author = {Lionel Rosier and Eduardo D. Sontag},
journal= {arXiv preprint arXiv:math/9912007},
year = {2007}
}
Comments
Related papers can be found in http://www.math.rutgers.edu/~sontag