  This paper presents a novel method for stability analysis of a wide class of
linear, time-delay systems (TDS), including retarded non-neutral ones, as well
as those incorporating incommensurate and distributed delays. The proposed
method is based on frequency domain analysis and the application of Rouche's
theorem. Given a parametrized TDS, and some parametric point for which the
number of unstable poles is known, the proposed method is capable of
identifying the maximum surrounding region in the parametric space for which
the number of unstable poles remains invariant. First, a procedure for
investigating stability along a line is developed. Then, the results are
extended by the application of Holder's inequality to investigating stability
within a region. Contrary to existing approaches, the proposed method is
uniformly applicable to parameters of different types (delays, distributed
delay limits, time constants, etc.). Efficacy of the proposed method is
demonstrated using illustrative examples.
