On the instability of differential systems with varying delay

The unstable properties of the null solution of the nonautonomous delay system x (t ) = A(t)x(t) + B(t)x(t − r1(t )) + f (t,x(t),x(t − r2(t ))) are examined; the nonconstant delays r1, r2 are assumed to be continuous bounded functions. The case A = constant is reviewed, where a theorem, recalling the Perron instability theorem for ordinary differential equations, is obtained.  2002 Elsevier Science (USA). All rights reserved.