It is shown that any stabilizing, certainty equivalence control used within
an adaptive control system, causes the familiar interconnection of a contr
olled process and associated output estimator to be detectable through the
estimator's output error e(p), for every frozen value of the index or param
eter vector p upon which both the estimator and controller dynamics depend.
The fact that certainty equivalence implies detectability has been known f
or some time - this has been shown to be so whenever the process model is l
inear and the controller and estimator models are also linear for every fro
zen value of p. In this paper, use is made of recently introduced concepts
of input-to-state stability and detectability for nonlinear systems to prov
e that the same implication is valid in a more general, nonlinear setting.
(C) 1999 Published by Elsevier Science B.V. All rights reserved.