Transfer function with time delay (dead time)

The transfer function of the system is stable as it is seen in the figure? The denominator includes the exponential term is a violation of Routh Hurwitz criterion. I also did not draw the unit step response of the system. How do we implement a stability test for this system in Matlab? (BIBO, Lyapunov, etc.)

Answer 1

[Sebastian Castro]

You can make a linear approximation of those time delays (Exponentials in the frequency domain) using the Pade Approximation:

http://www.mathworks.com/help/control/ref/pade.html

Once you have your linear systems, you can just look at the poles of the system to determine (approximate) stability.

- Sebastian