Generalized sensitivity functions for multiple output systems

The main purpose of this paper is to introduce the concept of generalized sensitivity matrices extending the usual concept of generalized sensitivity functions. We consider systems with finitely many measurable outputs, because this case occurs frequently. It is demonstrated that the generalized sensitivity matrix can be interpreted as the Jacobian of the estimated parameters with respect to the nominal parameter vector. This interpretation is supported by numerical results for two examples, the Verhulst–Pearl logistic growth model, which as been used frequently in the context of generalized sensitivity functions, and the so-called minimal model for the intravenous glucose tolerance test, which represents a system with two measurable outputs. Furthermore, we discuss the implications of linear behavior of the generalized sensitivity matrix at large sampling times for identifiability of system parameters.