  We present an application of the unitarity-based dispersion matrix (DM)
approach to the extraction of the CKM matrix element $|V_{cb}|$ from the
experimental data on the exclusive semileptonic $B_{(s)} \to D_{(s)}^{(*)} \ell
\nu_\ell$ decays. The DM method allows to achieve a non-perturbative,
model-independent determination of the momentum dependence of the semileptonic
form factors. Starting from lattice results available at large values of the
4-momentum transfer and implementing non-perturbative unitarity bound, the
behaviour of the form factors in their whole kinematical range is obtained
without introducing any explicit parameterization of their momentum dependence.
We consider the four exclusive semileptonic $B_{(s)} \to D_{(s)}^{(*)} \ell
\nu_\ell$ decays and extract $|V_{cb}|$ from the experimental data for each
transition. The average over the four channels is $|V_{cb}| = (41.2 \pm 0.8)
\cdot 10^{-3} $, which is compatible with the latest inclusive determination at
$1\sigma$ level. We address also the issue of Lepton Flavour Universality by
computing pure theoretical estimates of the $\tau/\ell$ ratios of the branching
fractions for each channel, where $\ell$ is a light lepton. In the case of a
light spectator quark we obtain $R(D^*) = 0.275(8)$ and $R(D) = 0.296(8)$,
which are compatible with the corresponding experimental values within
$1.3\sigma$. In the case of a strange spectator quark we obtain
$\textit{R}(D_s^*) =0.2497(60)$ and $\textit{R}(D_s) = 0.298(5)$. The different
values for $R(D_s^*)$ and $R(D^*)$ may reflect $SU(3)_F$ symmetry breaking
effects, which seem to be present in some of the lattice form factors,
especially at large values of the recoil.
