Sensitivity function of LTI fractional order dynamic systems with respect to the orders

Many real natural or man-made dynamic systems can be better characterized using a fractional order dynamic model. Since in such a case the order assumes a non-integer value, it is of interest to consider the effect of small perturbation around the nominal value. It is of practical importance to analyze the influence of the order variations on the system behavior. This paper establishes an analytical method for the analysis of the sensitivity function of LTI fractional order dynamic systems with respect to the orders. The continuous dependent condition of the orders of fractional Green´s function is derived, which is proved as a necessary and sufficient condition. The singularity of fractional Green´s functions is discussed. Several examples are included for illustration.