Necessary and Sufficient Stability Criteria for a Class of Fractional-Order Delayed Systems

A new method for the stability analysis of a large class of fractional-order delayed systems is proposed. The exact region of the delay that can stabilize the system is determined without any approximation. Two steps of system transformation are employed to switch the fractional characteristic function to its corresponding integral function and to achieve an algebraic equation that facilitates the computation. Finally, an example is given to prove the feasibility of the proposed method.