Finding Stability Bounds for Delayed Systems with Uncertain Parameters

This work addresses the problem of determining the stability picture of an uncertain system with a time delay in the feedback line. Using the Cluster Treatment of Characteristic Roots (CTCR) and the preparatory step, the Spectral Delay Space (SDS), this work proposes an iterative approach to draw the stability picture of the system by effectively running the CTCR procedure for different points on a defined grid of values of the uncertainty. The technique presented in this work focuses on the appearance of purely imaginary roots to draw an exact stability picture of a system. Moreover, a case study of a portal crane with uncertainty in the lifted mass is presented to exemplify the results of this approach.