  We present a numerical method to analyze the relative stability of
closed-loop single-input-single-output (SISO) dead-time systems on a given left
complex half-plane for all positive delays. The well-known boundary crossing
method for the imaginary axis is extended to a given vertical line stability
boundary in the complex plane for these type of systems. The method allows to
compute the characteristic roots crossing the relative stability boundary and
their corresponding delays up to a maximum predefined delay. Based on this
method, we analyze the relative stability of the closed-loop system for all
positive delays. Both numerical methods are effective for high-order SISO
dead-time systems.
