Stability in n-dimensional differential-delay equations

AbstractIn this paper we give a sufficient condition for the zero solution of an n-dimensional differential-delay equation of the form ẋ(t) = A(t) x(t − r(t, xt)) to be uniformly stable. A sufficient condition for all solutions to go to zero is also stated. Although various theorems are known for characterizing stability and asymptotic stability in terms of “Liapunov” functions, it is, in general, very difficult to determine whether or not stability is present for a given system. The techniques of this paper enable one to deal with some specific nonautonomous equations in higher dimensions