Differential stability of convex discrete optimal control problems in Banach
spaces is studied in this paper. By using some recent results of An and Yen (Appl. Anal. 94,
108–128, 2015) on differential stability of parametric convex optimization problems under
inclusion constraints, we obtain an upper estimate for the subdifferential of the optimal
value function of a parametric convex discrete optimal control problem, where the objective
function may be nondifferentiable. If the objective function is differentiable, the obtained
upper estimate becomes an equality. It is shown that the singular subdifferential of the just
mentioned optimal value function always consists of the origin of the dual space.