2-D stability test for time-delay systems

It is difficult to determine the stability of time-delay systems, because the number of eigenvalues of the systems is infinite. To solve the problem of stability test of the systems, we develop a 2D approach for the stability test of time-delay systems. Constructing a 2D s-z hybrid polynomial based on the characteristic polynomial of given time-delay system, we show that the stability of the 2D polynomial can ensure the delay system to be stable, and provide a 2D Routh-Schur test for the stability of 2D s-z hybrid polynomial. Examples have been given to demonstrate the applicability of our new approach.