  This paper proposes a method to compute lower performance bounds for
discrete-time infinite-horizon min-max control problems with input constraints
and bounded disturbances. Such bounds can be used as a performance metric for
control policies synthesized via suboptimal design techniques. Our approach is
motivated by recent work on performance bounds for stochastic constrained
optimal control problems using relaxations of the Bellman equation. The central
idea of the paper is to find an unconstrained min-max control problem, with
negatively weighted disturbances as in H infinity control, that provides the
tightest possible lower performance bound on the original problem of interest
and whose value function is easily computed. The new method is demonstrated via
a numerical example for a system with box constrained input.
