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A problematic issue in the Walton-Marshall method for some neutral delay systems

Abstract : This paper considers delay systems with characteristic equation being a quasi-polynomial with one delay and polynomials of degree one. It is shown that for a subclass of systems which have a chain of poles clustering the imaginary axis by the left, the procedure of Walton and Marshall fails: we prove the existence, for an infinitesimally small delay, of a positive real pole at infinity. This real pole is then proved to be the unique pole of the system in the closed right half-plane for all values of the delay. Some numerical examples illustrate the results.
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Submitted on : Tuesday, January 7, 2020 - 6:03:25 PM
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Vy Nguyen, Catherine Bonnet, Islam Boussaada, Marianne Souaiby. A problematic issue in the Walton-Marshall method for some neutral delay systems. CDC 2019 - 58th Conference on Decision and Control, Dec 2019, Nice, France. ⟨hal-02431270⟩

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