I recently stumbled across some notes on the "Waterbed effect" in some notes by A. Megretski for an MIT course on "multivariate control systems". Here's an excerpt:
A common effect, usually associated with unstable zeroes and poles of the open loop plant, makes it theoretically impossible to make certain closed loop transfer functions “small” simultaneously at all frequencies: if amplitude of the frequency response is reduced in one part of the spectrum, it may have to get larger in the other part. This effect, sometimes called the waterbed effect, can be explained mathematically in terms of integral inequalities imposed on the closed loop transfer functions. In the basis of such results is the affine characterization of all possible closed loop responses, as well as the Cauchy integral relation for analytical functions.
I don't think I've ever heard of this before. Could someone explain the effect in more practical terms? When am I likely to encounter this effect in practice?