Second Order Eigensensitivities of Singularly Perturbed Systems

Abstract

In this paper, second order eigenvalue sensitivities are derived with respect to the singular perturbation parameter whose variation changes the reduced system order. These sensitivities are used to identity boundaries between fast and slow subsystems. This is applicable to systems that possess two-time scale property. Accurate estimates for the system modes without solving the eigenproblem of the whole system are obtained.