NECESSARY CONDITIONS AND ALGORITHMIC STABILITY TESTS FOR CERTAIN HIGHER ODD ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

In this paper we obtain necessary conditions and robust algorithmic criteria for asymptotic stability of the zero solution of higher odd order linear neutral delay differential equations of the form y (2m+1)(t) + αy(2m+1)(t − τ) = X 2m j=0 ajy (j) (t) +X 2m j=0 bjy (j) (t − τ) where aj , bj, and α 6= 0 are real constants. Here τ > 0 is a constant delay. In proving our results we make use of Pontryagin’s theory for quasi-polynomials.