SYSTEM THEORETIC REPRESENTATIONS FOR LINEAR NETWORKS.

The system-theoretic representation of imittances of passive networks such as positive real functions, positive matrices, lossless positive real matrices, LC, RC and RL impedance functions was reported by R. Kalman, V. Yakubovich, B. Anderson, etc. This paper presents the system-theoretic representation of the RC and RL impedance matrices, as well as RC 3-terminal network transfer functions and all-pass transfer functions. The coefficient matrices of state equations of new transfer functions which are obtained from another transfer function via frequency transformation of s to 1/s and s plus 1/s are derived. Furthermore, the relation among matrix coefficients of non-minimal state space equations which describes constant-immittance networks are obtained. As for the RC and RL impedance matrices, a criterion for determining whether a given real rational matrix is RC or RL impedance matrix is given.