  We discuss the {\it nonlinear stability} of phase-locked states for globally
coupled nonlinear oscillators with finite inertia, namely the modified Kuramoto
model, in the context of the robust $\ell^{\infty}$-norm. We show that some
classes of phase-locked states are orbitally $\ell{\infty}$-stable in the sense
that its small perturbation asymptotically leads to only the phase shift of the
phase-locked state from the original one without changing its fine structures
as keeping the same suitable coupling strength among oscillators and the same
natural frequencies. The phase shift is uniquely determined by the average of
initial phases, the average of initial frequencies, and the strength of
inertia. We numerically confirm the stability of the phase-locked state as well
as its uniqueness and the phase shift, where various initial conditions are
considered. Finally, we argue that some restricted conditions employed in the
mathematical proof are not necessary, based on numerical simulation results.
