  We study the synchronized behavior of the inertial Kuramoto oscillators with
frustration effect under a symmetric and connected network. Due to the lack of
second-order gradient flow structure and singularity of second-order derivative
of diameter, we shift to construct convex combinations of oscillators and
related new energy functions that can control the phase and frequency
diameters. Under sufficient frameworks on initial data and system parameters,
we derive first-order dissipative differential inequalities of constructed
energy functions. This eventually gives rise to the emergence of frequency
synchronization exponentially fast.
