Fully characterization of strictly positive real transfer function matrices

Several necessary and sufficient conditions for characterization of strict positive realness property of transfer function matrices have been derived in the literature. However, some of them are inconsistent with definition of strict positive realness and the others have been restricted to proper transfer function matrices. Besides, there is a necessary condition in the previous correct statements which is difficult to check. In this paper, using Markov parameters of linear time invariant multivariable systems, we will remove the aforementioned deficiencies. On the other hand, we will prove new equivalent conditions to characterize strict positive realness such that not only it can be easily checked but also it can be used when the transfer function matrix is improper.