  Imaging Atmospheric Cherenkov Telescopes study the highest energy (up to tens
of TeV) photon emission coming from nearby and distant astrophysical sources,
thus providing valuable results from searches for Lorentz Invariance Violation
(LIV) effects. Highly variable, energetic and distant sources such as Pulsars
and AGNs are the best targets for the Time-of-Flight LIV studies. However, the
limited number of observations of AGN flares or of high-energy pulsed emission
greatly restricts the potential of such studies, especially any potential LIV
effects as a function of redshift. To address these issues, an inter-experiment
working group has been established by the three major collaborations taking
data with Imaging Atmospheric Cherenkov Telescopes (H.E.S.S., MAGIC and
VERITAS) with the aim to increase sensitivity to any effects of LIV, together
with an improved control of systematic uncertainties, by sharing data samples
and developing joint analysis methods. This will allow an increase in the
number of available sources and to perform a sensitive search for redshift
dependencies. This presentation reviews the first combined maximum likelihood
method analyses using simu- lations of published source observations done in
the past with H.E.S.S., MAGIC and VERITAS. The results from analyses based on
combined maximum likelihood methods, the strategies to deal with data from
different types of sources and instruments, as well as future plans will be
presented.
