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UMINF 11.11

Stratification of Full Rank Polynomial Matrices

We analyze the perturbations of polynomial matrices of full normal-rank via the study of perturbations of linearizations of such polynomial matrices. We show that a full normal-rank polynomial matrix has the same structural elements as its right (or left) linearization. Furthermore, the linearized pencil has a special structure that can be taken into account when studying its stratification. This yields constraints on the set of achievable eigenstructures. We explicitly show which these constrains are. These results allow us to derive necessary and sufficient conditions for cover relations between two orbits or bundles of the linearization of full normal-rank polynomial matrices. The result is exemplified on two mechanical systems: A controlled uniform platform with two degrees of freedom and a half-car passive suspension system with four degrees of freedom.


polynomial matrices, matrix pencils, linearization, perturbations, stratification, closure hierarchy, cover relations, StratiGraph


Stefan Johansson , Bo Kågström and Paul Van Dooren

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Entry responsible: Stefan Johansson

Page Responsible: Frank Drewes