Dissipative Control Systems and Disturbance Attenuation for Nonlinear H ^∞ Problems

Abstract.

We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H ^∞ problem from contingent formulation of Isaacs' equation.