  This work is concerned with the stability of regime-switching processes under
the perturbation of the transition rate matrices. From the viewpoint of
application, two kinds of perturbations are studied: the size of the transition
rate matrix is fixed, and only the values of entries are perturbed; the values
of entries and the size of the transition matrix are all perturbed. Moreover,
both regular and irregular coefficients of the underlying system are
investigated, which clarifies the impact of the regularity of the coefficients
on the stability of the underlying system.
