  This paper characterizes the solution to a finite horizon min-max optimal
control problem where the system is linear and discrete-time with control and
state constraints, and the cost quadratic; the disturbance is negatively
costed, as in the standard H-infinity problem, and is constrained. The cost is
minimized over control policies and maximized over disturbance sequences so
that the solution yields a feedback control. It is shown that the value
function is piecewise quadratic and the optimal control policy piecewise
affine, being quadratic and affine, respectively, in polytopes that partition
the domain of the value function.
