The Quadratic Eigenvalue Problem

Abstract

Thus far we have studied the damped system through its phase space matrix A by taking into account its J-Hermitian structure and the underlying indefinite metric. Now we come back to the fact that this matrix stems from a second order system which carries additional structure commonly called ‘the quadratic eigenvalue problem’.We study the spectrum of A and the behaviour of its exponential over time. A special class of so-called overdamped systems will be studied in some detail.