We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate
additive fractional Brownian motion with arbitrary Hurst parameter \(H\in(0,1)\). A
general framework is constructed to make precise the notions of ``invariant measure''
and ``stationary state'' for such a system. We then prove under rather weak dissipativity
conditions that such an SDE possesses a unique stationary solution and that the convergence
rate of an arbitrary solution towards the stationary one is (at least) algebraic.
A lower bound on the exponent is also given.