  In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras
and give some characterizations and new constructions. Then we construct a
graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter
systems. This allows us to define a cohomology theory associated with a
relative Rota-Baxter system. Finally, we study formal deformations and
extendibility of finite order deformations of a relative Rota-Baxter system in
terms of the cohomology theory.
