Spectral conditions for positive realness of single-input-single-output systems

In this note, we derive necessary and sufficient conditions for a single-input-single-output system to be (strictly) positive real. These conditions take the form of a spectral condition on a matrix product constructed from the state space representation of the linear time-invariant system {A,b,c,d}. Numerical examples are given to illustrate the usefulness of our conditions.