Advanced clustering with frequency sweeping (ACFS) methodology for the stability analysis of multiple time-delay systems

A novel methodology, Advanced Clustering with Frequency Sweeping (ACFS), is introduced for the stability analysis of the most general class of linear time-invariant (LTI) time-delay systems (TDS) with multiple delays. Different from the literature, ACFS does not impose any restrictions in system order, the number of delays and the ranks of the system matrices in the LTI-TDS considered. An unmatched strength of ACFS is that it can achieve to directly extract the 2D cross-sections of the stability views in the domain of any of the two delays. ACFS owes this superiority to an elegant way of cross-fertilizing the resultant theory, frequency sweeping technique, and the root clustering paradigms. ACFS also proposes a new formula that can compute the precise lower and upper bounds of the only parameter, the frequency, that it sweeps. Case studies that are prohibitive to analyze with the existing methods are presented to demonstrate the strengths of ACFS.