Stability of linear systems in second-order form based on structure preserving similarity transformations

Abstract

This paper deals with two stability aspects of linear systems of the form \({I\ddot{x}+B\dot{x}+Cx=0}\) given by the triple (I, B, C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I, B1, C1) with a symmetrizable matrix C1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.