Stabilization of time delay systems
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In this paper, we first consider the problem of stabilizing a first-order plant with dead time using a constant gain controller. Using a version of the Hermite-Biehler Theorem applicable to quasipolynomials, a complete analytical characterization of all stabilizing gain values is provided as a closed form solution. A similar approach is then used to tackle the problem of stabilizing a first-order plant with time delay using a PI controller, and once again the complete stabilizing set is determined.