Some inverse eigenvalue and pole placement problems for linear and quadratic pencils

Abstract

Differential equation models for vibrating systems are associated with matrix eigenvalue problems. Frequently the undamped models lead to problems of the generalized eigenvalue type and damped models lead to problems of the quadratic eigenvalue type. The matrices in these systems are typically real and symmetric and are quite highly structured. The design and stabilisation of systems modelled by these equations (eg., undamped and damped vibrating systems) requires the determination of solutions to the inverse eigenvalue problems which are themselves real, symmetric and possibly have some other structural properties. In this talk we consider some pole assignment problems and inverse spectral problems for generalized and quadratic symmetric pencils, discuss some advances and point to some work that remains to be done. © 2011 Springer Science+Business Media B.V.