  We study perturbations of topological pressures, Gibbs measures and
measure-theoretic entropies of these measures concerning perturbed potentials
defined on topologically transitive subshift of finite type. The subshift with
respect to non-perturbed system is assumed to be no topologically transitive.
Therefore, the subshift of the perturbed systems and the subshift of the
unperturbed system are different. We reduce this situation to a perturbation
problem of certain irreducible nonnegative matrices generated by Ruelle
transfer operators. Consequently, under suitable conditions of potentials, we
characterize the limit points of those thermodynamics and give a necessary and
sufficient condition for convergence of Gibbs measures and the
measure-theoretic entropy of this measure when the subshift of the
non-perturbed system has $2$ or $3$ transitive components with the maximal
pressure. Finally, we illustrate the relation between potentials and
convergence of Gibbs measures by using asymptotic expansion techniques for
eigenvalues of Ruelle transfer operators.
