  We construct noncommutative multidimensional versions of overconvergent power
series rings and Robba rings. We show that the category of \'etale
$(\varphi,\Gamma)$-modules over certain completions of these rings are
equivalent to the category of \'etale $(\varphi,\Gamma)$-modules over the
corresponding classical overconvergent, resp. Robba rings (hence also to the
category of $p$-adic Galois representations of $\mathbb{Q}_p$). Moreover, in
the case of Robba rings, the assumption of \'etaleness is not necessary, so
there exists a notion of trianguline objects in this sense.
