Waterbed effect

The waterbed effect is the phenomenon in feedback control systems whereby reducing the sensitivity function in one frequency band necessarily increases it in another. Like pressing on a waterbed, pushing sensitivity down in one place causes it to rise elsewhere. The effect is governed by Bode's integral theorem, a conservation law for feedback systems that states the integral of logarithmic sensitivity over all frequencies is fixed by the system's unstable poles. The waterbed effect is not an engineering inconvenience; it is a topological constraint on all self-correcting systems, from thermostats to central banks.

See also: Sensitivity function, Control theory, Bode's integral theorem, Robust control