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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, BR, 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.

 

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