On the Characterization of Strict Positive Realness for General Matrix Transfer Functions

We present conditions which are necessary and sufficient for a transfer function (or transfer function matrix) to be strictly positive real. A counter-example is given to illustrate that the conditions presented here differ from those previously presented in the literature. The proof of our results differs from previous related proofs in that it only uses properties of analytic functions and matrices and does not require state-space realizations. Also, the results are not restricted to rational transfer functions with real coefficients.