Multi-parameter structural transformations of passive electrical networks and natural frequency assignment

The paper examines the problem of systems redesign within the context of passive electrical networks by considering the problem of multi-parameter changes, their representation and impact on properties such as characteristic frequencies. The general problem area is the modelling of systems, whose structure is not fixed but evolves during the system lifecycle. The specific problem we are addressing is the study of effect of changing the topology of an electrical network that is changing individual elements of the network into elements of different type and value, augmenting / or eliminating parts of the network and developing a framework that allows the study of the effect of such transformations on the natural frequencies. This problem is a special case of the more general network redesign problem. We use the Impedance-Admittance models and we establish a representation of the different types of transformations on such models. For the case of network cardinality preserving transformations, we formulate the natural frequencies assignment problem as a problem of zero assignment of matrix pencils by additive structured transformations and this allows the deployment of the Determinantal Assignment Problem framework for the study of assignment and determination of fixed natural frequencies.