Location of zeros of some classes of quasi-polynomials for the stabilituy stiudy of dynamical systems with delay*

Abstract: In this talk we will consider delay systems with characteristic equation being a quasi-polynomial with one delay and polynomials of degree n. Contrary to what is admitted in the delay systems litterature, a subclass of quasi-polynomials is shown to possess a real zero at infinity when the delay appears. By applying the Argument Principle to a carefully chosen contour enclosing the right half-plane we even prove that this real zero is the the unique zero of the quasi-polynomial in the closed right half-plane for all values of the delay. Some numerical examples illustrate the results.

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