Abstract

In a seminal paper Foster (1924) showed that the impedances of lumped electrical circuits generated by inductances and capacitors are positive real odd functions ( PRO for short). For multi-port electrical systems built from inductances and capacitors one obtains matrix-valued PRO functions, denoted PRO m in the case of to × to matrix functions. Like PRO , the class of matrix functions PRO m is also a convex invertible cone, i.e., a convex cone closed under inversion (in the form of involution). Given a minimal, Weierstrass descriptor realization for a function in PRO m , we explicitly compute a minimal, Weierstrass descriptor realization for its involution, and through these formulas we analyse the zero-pole structure of the function.

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