Non-zero set-point affine feedback control of impulsive systems with application to biomedical processes

Abstract

Linear impulsive systems have been extensively studied in the last decades, mainly in the field of biomedical research. However, a proper characterisation of the equilibria of such a systems - when they are out of the origin - and its use by optimising control strategies is still a matter of discussion. In this work, a novel characterisation of the system equilibria and invariant regions - derived from the definition of two underlying discrete-time systems - is given, and based on this characterisation impulsive affine feedback control strategies for non-zero set-points are designed. The closed-loop performance and benefits of the strategies are assessed through two biomedical examples: the Lithium ions distribution in the human body and the HIV treatment.