New Results on the Characterization of Strictly Positive Real Matrix Transfer Functions

In this article, we analyze the high-frequency condition that discriminates strictly positive real systems from weakly strictly positive real ones. Different versions of this condition have been proposed in the literature. We consider the general case of multi-input-multi-output (MIMO) systems and derive new equivalent conditions. A graphic interpretation is also presented. In comparison to the existing literature, the conditions derived here are easier to check, especially for large dimension systems and high-order systems. Several illustrative examples are provided to support the results.