Rt. Mcloskey, AN AVERAGING THEOREM FOR TIME-PERIODIC DEGREE ZERO HOMOGENEOUS DIFFERENTIAL-EQUATIONS, Systems & control letters, 32(3), 1997, pp. 179-183
This paper considers the stability of the differential equation (x) ov
er dot=epsilon X(t,x,epsilon), x is an element of R-n, where X(t,x,eps
ilon) is a time-periodic, degree zero homogeneous vector field and eps
ilon>0 is a parameter. It is shown that asymptotic stability of the ti
me-averaged equation implies asymptotic stability of the original syst
em for epsilon sufficiently small. (C) 1997 Elsevier Science B.V.