  We first introduce the calculus of Peng's G-Brownian motion on a sublinear
expectation space $(\Omega, {\cal H}, \hat{\mathbb{E}})$. Then we investigate
the exponential stability of paths for a class of stochastic differential
equations disturbed by a G-Brownian motion in the sense of quasi surely (q.s.).
The analyses consist in G-Lyapunov function and some special inequalities.
Various sufficient conditions are obtained to ensure the stability of strong
solutions. In particular, by means of our results we generalize the one in the
classical stochastic differential equations. Finally, an illustrative example
is given.
