Stability analysis of multiple time delayed systems using 'building block' concept

Abstract

An intriguing perspective is presented in studying the stability robustness of systems with multiple independent and uncertain delays. It is based on a very practical mapping, that creates a dramatic reduction in the dimension of the problem from infinity to manageably small. In essence, this mapping collapses the entire set of potential stability switching points onto a small (upperbounded) number of building hypersurfaces within, what we call a building block. We demonstrate that these building hypersurfaces can be implicitly defined and it is also shown that the exhaustive detection of these building hypersurfaces is necessary and sufficient in order to arrive at the complete stability robustness picture in the domain of the delays. This novel perspective serves very well for the preparatory steps of the authors' earlier contribution in the area, cluster treatment of characteristic roots (CTCR). A complete example case study is also provided