Volume 2, Number 2, Spring 1994
STABILITY WITH RESPECT TO THE DELAY
IN A CLASS OF DIFFERENTIAL-DELAY EQUATIONS
F.G. BOESE AND P. VAN DEN DRIESSCHE
Abstract. The locations of the zeros of the characteristic
function associated with a differential-delay equation with
constant parameters govern its stability. For the class considered,
this function has the form A(z) + Be-Tz where A(z)
is a real, strongly damped polynomial of degree n, B ∈ R,
and T ≥ 0 is the delay. By focusing on the effects of the
delay, necessary and sufficient conditions for stability are derived.
Examples are explicitly given for n = 2 (a case which
occurs in many applications) and n = 3. The class is extended
to more general functions A(z) + B·B(z)-Tz for restricted
polynomials B(z) of degree m < n.