On l^∞ to l^∞ performance of slowly varying systems

In this paper we present a result on the l^∞ to l^∞ performance of slowly time varying systems. In particular we show that the performance of such systems cannot be much worse than that of the frozen-time systems which are time invariant. We also demonstrate via an example that optimal frozen-time design may in general result to far from optimal l^∞ to l^∞ performance even though the time variations of the system can be arbitrarily slow.