A common problem of interest is that of controlling a stochastic process so as to keep the state in some fixed set G. The two optimization criteria which are most often used are the escape probability over a fixed time interval and the mean escape time. We apply a risk-sensitive criterion to the escape problem which avoids certain difficulties associated with the above two criteria. Further, in the risk-averse limit the value function converges to the value of a deterministic differential game where an opposing player attempts to push the process out of G. In analogy with H/sup /spl infin// disturbance rejection bounds, this yields a lower bound on the escape time as a (nonlinear) function of the L/sup 2/ norm of the opposing player's control. >