Nullor network Jacobian and Hessian matrices: symbolic determination by using Chan-Mai signal-flow graphs

摘要

A topological method for obtaining Jacobian and Hessian matrices of active networks is presented. It is based on the replacement of the investigated network by using a or equivalent circuit and on the representation of the circuit passive part by a Chan-Mai signal-flow graph (CMSFG). The Jacobian and the Hessian matrix elements of the or network can be obtained by means of some dependent variables of two or four isomorphic CMSFGs, respectively. Two examples illustrate the proposed method.