Zero Structure Assignment Of Matrix Pencils: The Case Of Structured Additive Transformations

Abstract

Matrix Pencil Models are natural descriptions of linear networks and systems. Changing the values of elements of networks, that is redesigning them implies changes in the zero structure of the associated pencil by structured additive transformations. The paper examines the problem of zero assignment of regular matrix pencils by a special type of structured additive transformations. For a certain family of network redesign problems the additive perturbations may be described as diagonal perturbations and such modifications are considered here. This problem has certain common features with the pole assignment of linear systems by structured static compensators and thus the new powerful methodology of global linearisation [1, 2] can be used. For regular pencils with infinite zeros, families of structured degenerate additive transformations are defined and parameterised and this lead to the derivation of conditions for zero structure assignment, as well as methodology for computing such solutions. Finally the case of regular pencils with no infinite zeros is considered and conditions of zero assignment are developed. The results here provide the means for studying certain problems of linear network redesign by modification of the non-dynamic elements.