Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in H-infinity control

This paper deals with the regularity of solutions of the :Hamilton-Jacobi i nequality which arises in H-infinity control. It shows by explicit countere xamples that there are gaps between existence of continuous and locally Lip schitz (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 in crease in gain is allowed. (C) 2000 Elsevier Science B.V. All rights reserv ed.