Partial identification of underdetermined compartmental models: A method based on positive linear Lyapunov functions

A class of models is considered in which the number of unknown parameters exceeds the number of independent equations that are derived from the input/observation configuration. It is shown that, under certain circumstances, if the number of unknown parameters is sufficiently decreased by setting some of the exit parameters to zero, then the fallaciously derived model has the following interesting properties. The functions of time that give the amounts in the compartments are constant multiples of their counterparts in the fallacious model. A subset of the fallacious fractional transfer coefficients have the same values as their counterparts in the true model whereas others yield interval bounds. These and related results are obtained from a method based on positive linear Lyapunov functions.