Stability and Stabilization of Retarded Fractional Delay Differential Systems

The main objective of this paper is twofold. First, we devise a stability test for determining whether a linear retarded fractional delay differential system has no characteristic roots in a specified right half of the complex plane. Second, we develop a practical method for computing the abscissa of stability (defined as the largest of the real parts of the characteristic roots) for this type of system. The method is based on a known technique which makes repeated use of a stability test, thereby avoiding the calculation of all the roots. The stability test and the method for computing the abscissa of stability provide useful computational tools for the design of fractional differential systems using the method of inequalities as well as other numerical optimization approaches. Numerical examples are also given.