Abstract
This paper considers the problem of stabilizing a first-order plants with known time delay using a fractional-order proportional-integral controller PI lambda. Using a generalization of the Hermite-Biehler theorem applicable to quasi-polynomials, a complete analytical characterization of all stabilizing gain values (k(p), k(i)) is provided. The widespread industrial use of fractional PI controllers justifies a timely interest in PIl tuning techniques.