  This paper is devoted to the study of perturbations of a matrix pencil,
structured or unstructured, such that a perturbed pencil will reproduce a given
deflating pair while maintaining the invariance of the complementary deflating
pair. If the latter is unknown, it is referred to as no spillover updating. The
specific structures considered in this paper include symmetric, Hermitian,
$\star$-even, $\star$-odd and $\star$-skew-Hamiltonian/Hamiltonian pencils.
This study is motivated by the well-known Finite Element Model Updating Problem
in structural dynamics, where the given deflating pair represents a set of
given eigenpairs and the complementary deflating pair represents the remaining
larger set of eigenpairs. Analytical expressions of structure preserving no
spillover updating are determined for deflating pairs of structured matrix
pencils. Besides, parametric representations of all possible unstructured
perturbations are obtained when the complementary deflating pair of a given
unstructured pencil is known. In addition, parametric expressions are obtained
for structured updating with certain desirable structures which relate to
existing results on structure preservation of a symmetric positive definite or
semi definite matrix pencil.
