Stabilization of some fractional neutral delay systems which possibly possess an infinite number of unstable poles

Abstract : We consider fractional delay systems of neutral type and prove that many systems with infinitely many unstable poles cannot be stabilized by the class of rational fractional controllers of commensurate order. For a class of fractional neutral delay systems with an infinite number of poles asymptotic to the imaginary axis from the right or left hand side, we are able to derive a parametrization of all stabilizing controllers from fractional PI controllers obtained from previous work.