An inverse quadratic eigenvalue problem for damped gyroscopic systems

Abstract

ABSTRACT Model updating for damped gyroscopic systems can be mathematically formulated as the following inverse quadratic eigenvalue problem (IQEP) and an optimal approximation problem (OAP). Problem IQEP: Given , where p<n, and both Λ and X are closed under complex conjugation. Find real symmetric matrices and a real skew-symmetric matrix G (that is, ) such that Problem OAP: Given symmetric matrices and a skew-symmetric matrix , find such that where is the solution set of Problem IQEP. The representation of the general solution of Problem IQEP is deduced and the optimal approximation solution of Problem OAP is obtained.