  Let $(\Sigma_T,\sigma)$ be a subshift of finite type with primitive adjacency
matrix $T$, $\psi:\Sigma_T \rightarrow \mathbb{R}$ a H\"older continuous
potential, and $\mathcal{A}:\Sigma_T \rightarrow \mathrm{GL}_d(\mathbb{R})$ a
1-typical, one-step cocycle. For $t \in \mathbb{R}$ consider the sequences of
potentials $\Phi_t=(\varphi_{t,n})_{n \in \mathbb{N}}$ defined by
$$\varphi_{t,n}(x):=S_n \psi(x) + t\log \|\mathcal{A}^n(x)\|, \: \forall n \in
\mathbb{N}.$$ Using the family of transfer operators defined in this setting by
Park and Piraino, for all $t<0$ sufficiently close to 0 we prove the existence
of Gibbs-type measures for the superadditive sequences of potentials $\Phi_t$.
This extends the results of the well-understood subadditive case where $t \geq
0$. Prior to this, Gibbs-type measures were only known to exist for $t<0$ in
the conformal, the reducible, the positive, or the dominated, planar settings,
in which case they are Gibbs measures in the classical sense. We further prove
that the topological pressure function $t \mapsto
P_{\mathrm{top}}(\Phi_t,\sigma)$ is analytic in an open neighbourhood of 0 and
has derivative given by the Lyapunov exponents of these Gibbs-type measures.
