Laboratory for Control, Learning, and Systems Biology

Papers by L. Rosier and E.D. Sontag

2000
  1. ▪L. Rosier, E.D. Sontag, "Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in H infinity control", Systems Control Lett., vol. 41, no. 4, pp. 237–249, 2000. pdf
    viscosity solutions · H-infinity control
    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.