Stability criteria for certain high odd order delay differential equations

In this paper we study the asymptotic stability of the zero solution of odd order linear delay differential equations of the form y ( 2 m + 1 ) ( t ) = ∑ j = 0 2 m a j y ( j ) ( t ) + ∑ j = 0 2 m b j y ( j ) ( t - τ ) , where a j and b j are certain constants and m ⩾ 1 . Here τ > 0 is a constant delay. In proving our results we make use of Pontryaginʹs theory for quasi-polynomials.