Abstract
This paper concerns the characterization of positive real (PR) matrices generated by substitutions (of the Laplace variable s) in scalar rational transfer functions by matrix PR functions. Our main results are restricted to both strongly strictly PR matrices (SSPR) and strictly bounded real matrices. As a way to illustrate our main results, we also include here a partial extension of both the Kalman–Yakubovich–Popov lemma (for SSPR systems of zero relative degree) and the circle criterion (for strictly PR systems of zero relative degree).
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