  In this paper we are concerned with generalised L 1-minimisation problems,
i.e. Bolza problems involving the absolute value of the control with a
control-affine dynamics. We establish sufficient conditions for the strong
local optimality of extremals given by the concatenation of bang, singular and
inactive (zero) arcs. The sufficiency of such conditions is proven by means of
Hamiltonian methods. As a byproduct of the result, we provide an explicit
invariant formula for the second variation along the singular arc.
