2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/88131This note provides a theorem showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, in the sense of egulation against disturbances or tracking signals in U, then S must ecessarily contain a subsystem which is capable of generating all the signals in U. It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components. Instead, one assumes that a ``signal detection'' property holds. The result was motivated by questions of adaptation in bacterial chemotaxis, but the general mathematical principle is of wide applicability.See http://www.math.rutgers.edu/~sontag for related work; to appear in Systems and Control LettersQuantitative MethodsMolecular Networkstext