The best linear approximation of nonlinear systems operating in feedback

In the literature the best linear approximation (BLA) has been defined and studied for nonlinear systems operating in open loop. The difficulty of the closed loop configuration is that the nonlinear distortions also perturb the input via the feedback loop. These input distortions bias the estimate of the BLA. To handle this problem we introduce a generalized definition of the BLA that is valid for nonlinear systems operating in feedback. The classical definition for open loop systems follows as a special case. A measurement procedure is proposed and illustrated on open loop gain measurements of an operational amplifier.