A method for internally positive realization of continuous time systems

The concept of Internally Positive Realization (IPR) of a system generalizes the idea of realization of a generic transfer function through combination of positive filters: an IPR is a positive state space representation, endowed with input, state and output transformations, that realizes the dynamics of a given generic (i.e. with no positivity constraint) system. Techniques for the construction of IPRs of discrete-time linear systems are available in the literature. This paper presents a method for the construction of IPRs for continuous-time systems, and provides a theoretical characterization of the stability of the resulting realization. The results presented are relevant in the field of positive continuous-time systems, like compartmental systems and for the implementation of analog filters using VLSI distributed RC interconnects.