On Strictly Positive Real Nonrational Transfer Matrices With a Pole at Infinity

In this paper we consider positive real linear systems with the only (mild) assumption that the associated transfer matrix is meromorphic at infinity. Under this only assumption, we establish two different conditions that are necessary and sufficient for the system to be strictly positive real and regular. These conditions are very easy to test/enforce even for non-rational transfer matrices. The main motivation for our work comes from the results on closed-loop stability of linear and non-linear systems.