  On any smooth algebraic variety over a $p$-adic local field, we construct a
tensor functor from the category of de Rham $p$-adic \'etale local systems to
the category of filtered algebraic vector bundles with integrable connections
satisfying the Griffiths transversality, which we view as a $p$-adic analogue
of Deligne's classical Riemann--Hilbert correspondence. A crucial step is to
construct canonical extensions of the desired connections to suitable
compactifications of the algebraic variety with logarithmic poles along the
boundary, in a precise sense characterized by the eigenvalues of residues;
hence the title of the paper. As an application, we show that this $p$-adic
Riemann--Hilbert functor is compatible with the classical one over all Shimura
varieties, for local systems attached to representations of the associated
reductive algebraic groups.
