Computing the robust H-infinity norm of time-delay LTI systems with real-valued and structured uncertainties

Abstract

In this paper a new method to calculate the robust (worst-case) H∞-norm of a linear time-invariant time-delay system with an arbitrary number of delays with uncertainties both in the system matrices and the delay parameters is presented. The proposed approach fully exploits the real-valued and structured nature of the uncertainties. As in real-life applications, uncertainties can influence more than one system matrix. The algorithm utilizes the relation between the robust H∞-norm and the pseudo-spectrum of an associated non-linear (delay) eigenvalue problem with both real and complex perturbations. More precisely it uses the Newton-bisection method to find the robust complex distance to instability of this eigenvalue problem which will be shown to be equal to the reciprocal of the robust H∞-norm.