Updating structured matrix pencils with no spillover effect on unmeasured spectral data and deflating pair

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