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We consider the problem of computing the (two-sided) Hausdorff distancebetween the unit $\ell_{p_{1}}$ and $\ell_{p_{2}}$ norm balls in finitedimensional Euclidean space for $1 \leq p_1 < p_2 \leq \infty$, and derive aclosed-form formula for the same. We also derive a closed-form formula for theHausdorff distance between the $k_1$ and $k_2$ unit $D$-norm balls, which arecertain polyhedral norm balls in $d$ dimensions for $1 \leq k_1 < k_2 \leq d$.When two different $\ell_p$ norm balls are transformed via a common linear map,we obtain several estimates for the Hausdorff distance between the resultingconvex sets. These estimates upper bound the Hausdorff distance or itsexpectation, depending on whether the linear map is arbitrary or random. Wethen generalize the developments for the Hausdorff distance between twoset-valued integrals obtained by applying a parametric family of linear maps todifferent $\ell_p$ unit norm balls, and then taking the Minkowski sums of theresulting sets in a limiting sense. To illustrate an application, we show thatthe problem of computing the Hausdorff distance between the reach sets of alinear dynamical system with different unit norm ball-valued inputuncertainties, reduces to this set-valued integral setting.

A Note on the Hausdorff Distance between Norm Balls and their Linear Maps