A Minimal State Map for Strictly Lossless Positive Real Behaviors

Abstract

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.