Physically meaningful Lyapunov modal contributions in linear systems

Abstract

This paper introduces a finite-time generalization of Lyapunov modal contributions (LMC) – a technique for energy-based selective modal analysis. The main focus is a case study involving a system with physically meaningful squared output and considering its unforced movement as transferring excessive energy towards its environment. This problem statement leads to LMCs estimating energy transfers measured in joules. The results facilitate solutions to several issues that occur in applications of methods based on Gramian spectral decomposition.