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.