  Yb$_2$Si$_2$Al may be a prototype for exploring different aspects of the
Shastry-Sutherland lattice, formed by planes of orthogonally coupled Yb ions.
Measurements of the magnetic susceptibility find incoherently fluctuating
Yb$^{3+}$ moments coexisting with a weakly correlated metallic state that is
confirmed by measurements of the electrical resistivity. Increasing signs of
Kondo coherence are found with decreasing temperature, including an enhanced
Sommerfeld coefficient and Kadowaki-Woods ratio that signal that the metallic
state found at the lowest temperatures is a Fermi liquid where correlations
have become significantly stronger. A pronounced peak in the electronic and
magnetic specific heat indicates that the coupling of the Yb moments to the
conduction electrons leads to an effective Kondo temperature that is
approximately 30 K. The valence of Yb$_2$Si$_2$Al has been investigated with
electron spectroscopy methods. Yb$_2$Si$_2$Al is found to be strongly
intermediate valent ($v_F=2.68(2)$ at 80 K). Taken together, these experimental
data are consistent with a scenario where a coherent Kondo lattice forms in
Yb$_2$Si$_2$Al from an incoherently fluctuating ensemble of Yb moments with
incomplete Kondo compensation, and strong intermediate valence character.
