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LPV embedding of nonlinear compartmental systems with endogenous control

Compartmental models are widely used in in many fields of science including pharmacokinetics, epidemiology, bioengineering, complexity theory, and even economics and the social sciences. The reason of such a success lies in their ability to describe the way materials or energies are transmitted among the compartments. Often, it is assumed that these exchanges depend linearly on the compartments. However, when a compartment exerts an inhibitory or stimulative action on the exchange rate between two other compartments, the related mass transfer is usually a nonlinear function of both the source and controlling compartment. This paper shows how, in many cases, the resulting nonlinear compartmental model can be embedded into a linear parameter varying (LPV) model, which allows us to exploit some recent results on LPV control. In particular, it is possible to design controllers that ensure stability under arbitrary parameter variations as well as point-wise optimal performance.