Linearization and exponential stability
  We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is Fr\'{e}chet differential at the equilibrium, if it is only Gateaux differentiable, then we show by means of an example that the result does not hold. 
Hans Zwart
math.FA math.OC