Partial Eigenvalues Assignment in Singular Systems Using Brauer and Rado Eigenvalue Embedding for Impulse Elimination

Abstract

A partial infinite eigenvalues assignment for singular systems is proposed, inspired by the well-known Brauer theorem for eigenvalue embedding. Removal of infinite eigenvalues is a frequent practice in mechanical systems, for instance, to avoid impulsive acceleration and dangerous jerk of the system degrees-of-freedom with null or highly unbalanced mass. Recent efforts were delivered to extend the Brauer theorem to the generalized singular regular eigenvalue problem. However, removing infinite eigenvalues is treated as a particular example by taking the reciprocal pencil and removing its null eigenvalues. In this note, proof for partial infinite eigenvalues removal is made directly in the original regular singular pencil by updating the descriptor matrix, with no need to take the reciprocal pencil. Multi-step and single-step procedures for impulsive response elimination using Brauer’s and Rado’s type finite eigenvalues embedding are presented. The obtained results are effective, as illustrated in a numerical example.