Leventides, J. and Karcanias, N. (2009). Zero assignment of matrix pencils by additive structured transformations. LINEAR ALGEBRA AND ITS APPLICATIONS, 431(8), pp. 13801396. doi: 10.1016/j.laa.2009.05.033
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 and this is achieved 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 systemsby structured static compensators and thus the new powerful methodology of global linearization [J. Leventides, N. Karcanias, Sufficient conditions for arbitrary Pole assignment by constant decentralised output feedback, Mathematics of Control for Signals and Systems 8 (1995) 222–240; J. Leventides, N. Karcanias, Global asymptotic linearisation of the pole placement map: A closed form solution for the constant output feedback problem, Automatica 31 (1995) 1303–1309] can be used. For regular pencils with infinite zeros, families of structured degenerate additive transformations are defined and parameterized and this lead to the derivation of conditions for zero structure assignment, as well as methodology for computing such solutions. The case of regular pencils with no infinite zeros is also considered and conditions of zero assignment are developed. The results here provide the means for studying problems of linear network redesign by modification of the nondynamic elements.

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