A main contribution of this paper is the development of a Hopfield network-based algorithm for the fault diagnosis of the actuators in linear system with uncertainties. An unknown input decoupling approach is introduced to the design of an adaptive observer so that the observer is insensitive to uncertainties. As a result, the output observation error equation does not depend on the effect of uncertainties. Simultaneous energy minimization by the Hopfield network is used to minimize the least mean square of errors of errors of estimates of output variables. The Hopfield network provides an estimate of the gains of the actuators. When the system dynamics changes, identified gains go through a transient period and this period is used to detect faults. The proposed scheme is demonstrated through its application to a simulated second-order system.