A continuous system with time delay, is described by characteristic equation [ s^{2}+s+e^{-s mathrm{~T}}=0 ] Now, consider

Question:

A continuous system with time delay, is described by characteristic equation

\[
s^{2}+s+e^{-s \mathrm{~T}}=0
\]

Now, consider the following statements.

I. Strictly speaking, this equation has an infinite number of roots.

II. Approximate stability analysis is possible by replacing \(e^{-s T}\) in the equation by first two terms of its Taylor series, that is \(e^{-s \mathrm{~T}}=1-s \mathrm{~T}\).

III. T must be less than 1 to preserve the stability.

Of these statements
(a) I, II and III all are correct
(b) only II and III are correct
(c) only III is correct
(d) only I and II are correct.