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). The ensuing method, which we name the direct method ( DM), offers several unique features: It returns the number of unstable characteristic roots of the system in an explicit and non-sequentially evaluated function of time delay, τ. Consequently, the direct method creates exclusively all possible stability intervals of τ. Furthermore, it is shown that this method inherently verifies a widely accepted necessary condition for the τ-stabilizability of a LTI-NTDS. In the core of the DM lie a root clustering paradigm and the strength of Rekasius transformation in mapping a transcendental characteristic equation into an equivalent rational polynomial. In addition, we also demonstrate by an example that DM can tackle systems with unstable starting posture for τ=0, only to stabilize for higher values of delay, which is rather unique in the literature.
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