Positive real and strictly positive real MIMO systems: theory and application

The paper is dealing with the concept of positive real and strictly positive real properties of linear time-invariant systems. Although strict positive realness is the most important subset of positive real systems and extensively used in stabilizing control systems, there are inconsistencies in the literature for its necessary and sufficient conditions. Also, many frequency properties of such systems are less attended by the scholars. In this paper, a comprehensive discussion on definitions, properties, lemmas, and theorems related to multi-input multi-output positive real and strictly positive real systems will be presented. Further, several frequency domain properties are presented to characterize these functions. Also, three equivalent high frequency condition presented in the literature for strictly positive real systems are compared. The main results have been supported via several illustrative examples.