  In this paper, we have emphasized the stability analysis of the accelerating
cosmological models obtained in $f(T)$ gravity theory. The behavior of the
models based on the evolution of the equation of state parameter shows
phantom-like behavior at the present epoch. The scalar perturbation technique
is used to create the perturbed evolution equations, and the stability of the
models has been demonstrated. Also, we have performed the dynamical system
analysis for both the models. In the two specific $f(T)$ gravity models, three
critical points are obtained in each model. In each model, at least one
critical point has been observed to be stable.
