Adaptation and regulation with signal detection implies internal model

This note provides a simple result showing, under suitable technical assumptions, that if a systemadapts to a class of external signals U, in the sense of regulation against disturbances or tracking signals in U, thenmust necessarily 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. c � 2003 Elsevier Science B.V. All rights reserved.