Stability Domains Of Time-Delay Control Systems Containing Uncertain Parameters

In this paper, the stability of time-delay control systems subject to parameter perturbation is investigated. The maximum allowable perturbation in the parameters of the system that maintains stability is determined. The parameters are allowed to perturb inside an lp-hypersolid (such as a hyperellipsoid, a box or a diamond in a multi-dimensional space) around their nominal values, and the size of the largest hypersolid that preserves the stability conditions is computed. The stability is characterized as the location of the closed-loop poles inside the symmetric regions in the complex plane (so-called “D-stability”). A direct numerical method is developed for the calculation of these stability margins. The method requires plotting a distance function over the contour of the stability region and finding its minimum. To illustrate the method, a numerical example is provided.