A practical method for analyzing the stability of neutral type LTI-time delayed systems. (English) Zbl 1050.93065
Summary: 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 \(\tau\). Consequently, the direct method creates exclusively all possible stability intervals of \(\tau\). Furthermore, it is shown that this method inherently verifies a widely accepted necessary condition for the \(\tau\)-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 \(\tau=0\), only to stabilize for higher values of delay, which is rather unique in the literature.
Keywords:
linear systems with delays; linear neutral systems; delay-dependent stability; stability margins; cluster treatment of characteristic rootsReferences:
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