A unique methodology for the stability robustness of multiple time delay systems

The stability robustness is considered for linear time invariant (LTI) systems with rationally independent multiple time delays against delay uncertainties. The problem is known to be notoriously complex, primarily because the systems are infinite dimensional due to delays. Multiplicity of the delays in this study complicates the analysis even further. And “rationally independent” feature of the delays makes the problem prohibitively challenging as opposed to the TDS with commensurate time delays (where time delays are rationally related). A unique framework is described for this broadly studied problem and the enabling propositions are proven. We show that this procedure analytically reveals all possible stability regions exclusively in the space of the delays. As an added strength, it does not require the delay-free system under consideration to be stable. Our methodology offers a resolution to this question, which has been studied from variety of directions in the past four decades. None of these respectable investigations can, however, deliver an exact and exhaustive robustness declaration. From this stand point the new method has a unique contribution.