A Minimal State Map for Strictly Lossless Positive Real Behaviors

In this paper, behaviors with equal input and output cardinalities and with lossless positive real transfer functions corresponding to certain input-output partitions are considered. Based on Cauer synthesis method, an algorithm to obtain a minimal state map of such behaviors starting from an observable image representation is given. This algorithm makes use of polynomial algebraic methods to arrive at a minimal state map. It is shown that the algorithm has application in synthesis and analysis of lossless electrical networks.