It has recently been suggested that an isotropic singularity may be a generic feature of brane cosmologies, even in the inhomogeneous case. Using the covariant and gauge-invariant approach we present a detailed analysis of linear perturbations of the isotropic model F_b which is a past attractor in the phase space of homogeneous Bianchi models on the brane. We find that for matter with an equation of state parameter γ > 1, the dimensionless variables representing generic anisotropic and

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... neous perturbations decay as t→ 0, showing that the model F_b is asymptotically stable in the past. We conclude that brane universes are born with isotropy naturally built-in, contrary to standard cosmology. The observed large-scale homogeneity and isotropy of the universe can therefore be explained as a consequence of the initial conditions if the brane-world paradigm represents a description of the very early universe.