Dissipative Control Systems and Disturbance Attenuation for Nonlinear H - ProblemsH.FrankowskaauthorM.QuincampoixauthorWe characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of epicontingent and viscosity supersolutions to a Partial Differential Equation called the Hamilton-Jacobi-Bellman-Isaacs equation. Links between viscosity and epicontingent supersolutions are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H^{infty}-problem from contingent formulation of the Isaacs' Equation.1996-12WP-96-117Monograph