  The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $\vert V_{ub}\vert$ is
obtained from exclusive semileptonic $B \to \pi \ell \nu_\ell$ and $B_s \to K
\ell \nu_\ell$ decays adopting the unitarity-based dispersion matrix approach
for the determination of the hadronic form factors (FFs) in the whole
kinematical range. We use lattice computations of the relevant susceptibilities
and of the FFs in the large-$q^2$ regime in order to derive their behavior in
the low-$q^2$ region without assuming any specific momentum dependence and
without constraining their shape using experimental data. Then, we address the
extraction of $\vert V_{ub}\vert$ from the experimental data, obtaining $\vert
V_{ub}\vert = (3.62 \pm 0.47) \cdot 10^{-3}$ from $B \to \pi$ and $\vert
V_{ub}\vert = (3.77 \pm 0.48) \cdot 10^{-3}$ from $B_s \to K$, which after
averaging yield $\vert V_{ub}\vert = (3.69 \pm 0.34) \cdot 10^{-3}$. These
results are compatible with the most recent inclusive value $\vert V_{ub}
\vert_{incl} = 4.13\,(26) \cdot 10^{-3}$ at the 1$\sigma$ level. We also
present purely theoretical estimates of the ratio of the $\tau/\mu$ decay rates
$R^{\tau/\mu}_{\pi(K)}$, the normalized forward-backward asymmetry
$\bar{\mathcal{A}}_{FB}^{\ell,\pi(K)}$ and the normalized lepton polarization
asymmetry $\bar{\mathcal{A}}_{polar}^{\ell,\pi(K)}$.
