The exponential attractor is known as one of useful notions 
of invariant attractors in the theory of infinite-dimensional dynamical systems. 
It is also known that, if the semigroup of a dynamical system satisfies 
a compact perturbation condition of contraction, 
then the dynamical system has exponential attractors. 
In this paper, we clarify the meaning of the compact perturbation condition 
of contraction and show that the exponential attractor 
is a natural generalization of the exponentially stable equilibrium.