Brief A practical method for analyzing the stability of neutral type LTI-time delayed systems

Authors:
Nejat Olgac;Rifat Sipahi
Affiliations:
Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139, USA;Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139, USA
Venue:
Automatica (Journal of IFAC)
Year:
2004

Citing 2
Cited 1

Some simple criteria for stability of neutral delay-differential systems

Applied Mathematics and Computation
Complex Analysis for Mathematics and Engineering

Complex Analysis for Mathematics and Engineering

A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems

Automatica (Journal of IFAC)

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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, @t. Consequently, the direct method creates exclusively all possible stability intervals of @t. Furthermore, it is shown that this method inherently verifies a widely accepted necessary condition for the @t-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 @t=0, only to stabilize for higher values of delay, which is rather unique in the literature.