  We present in this work an analysis of Lorentz- and CPT-violating signals at
linear boost order in Penning-trap experiments. The theory of quantum
electrodynamics with Penning traps is revisited and the dominant shifts in the
cyclotron and anomaly frequencies of confined particles and antiparticles are
reproduced. To study time variations of the experimental signals at linear
boost order, we provide a general discussion on transformations of coefficients
for Lorentz violation between different frames, and derive the expressions of
the cyclotron and anomaly frequency shifts in the Sun-centered frame. Relating
these frequency shifts to the charge-to-mass ratios, the $g$ factors, and their
comparisons between particles and antiparticles, we extract numerous new or
improved bounds on coefficients for Lorentz violation from existing
Penning-trap measurements.
