Zero Assignment Problem in RLC Networks

Abstract

The paper deals with the problem of zero assignment in RLC networks by selection of appropriate values for the non- dynamical elements, the resistors. For a certain family of network redesign problems by the additive perturbations may be described as diagonal perturbations and such modifications are considered here. This problem belongs to the family of DAP problems (Determinantal Assignment Problem) and has common features with the pole assignment problem by decentralized output feedback and the zero assignment problem via structured additive perturbations. We demonstrate that the sufficient condition for generic zero assignment by selecting the resistors holds true. This condition is related to the rank of the differential of the related map and holds true generically when the degrees of freedom of the matrix of resistors exceeds the number of frequencies to be assigned (n > p + q). Using this result, we show through a generic example that the sufficient condition for the general zero assignment problems in RLC networks is satisfied and thus, zero assignment can be achieved via resistor determination.