Viscosity supersolutions of a class of Hamilton-Jacobi-Isaacs equations arising in nonlinear H/sup /spl infin// control

We consider the solvability of Hamilton-Jacobi-Isaacs equations that arise in nonlinear H/sup /spl infin// control problems where the system is affine in the control and disturbance, while the cost function is not necessarily continuous in the state and the control. We prove the existence of viscosity supersolutions under the assumption that the value function is finite. We also obtain global asymptotic stability of the closed-loop system under the H/sup /spl infin// controller and the worst-case disturbance.