Direct method for analyzing the stability of neutral type LTI-time delayed systems

Abstract A new paradigm is presented for assessing the stability posture of a general class of linear time invariant - neutral time delayed systems (LTI-NTDS). Unlike peer techniques, this novel method, called the Direct Method, offers a number of unique features: It returns exact bounds of time delay for stability including separated stability pockets: beyond that it gives the number of unstable characteristic roots of the system in an explicit function of time delay, τ. As a direct consequence of the latter feature, it creates exclusively all possible stability intervals of τ. Furthermore it is shown that the Direct Method inherently enforces a very popular necessary condition for the stabilizability of LTI-NTDS. In the core of the approach lies the strength of Rekasius transformation, which maps (exactly) the transcendental characteristic equation of LTI-NTDS into an equivalent rational polynomial form. In addition to the above listed unmatched characteristics of the Direct Method we also demonstrate that it can tackle systems with unstable starting posture for τ = 0, only to stabilize it for higher values of delay, which is rather unique in the literature.