Shadow technology was a highly advanced scientific field created by the mysterious Haydonites.
Shadow Technology was an ancient technology which, according to Veidt, had been long abandoned by the time of the Sentinels. This was later used by T.R. Edwards to avoid capture when fleeing Tirol. It is unclear if he was granted this by rogue Haydonites or if Veidt had been lying.
Shadow technology was initially believed to be have been developed by T.R. Edwards, who covertly equipped it to the battle cruiser Icarus as well as producing several squadrons of "Shadow fighters". Edwards used this new technology to assist in his escape from Tirol, preventing the REF forces from being able to lock their weapons on his vessels.
Thus, the REF strove to quickly develop its own Shadow technology to cancel Edwards' tactical advantages. To this end the Haydonites, as the most technologically advanced member of the Sentinels, offered to help the REF in this endeavor. (comic: "Robotech: Prelude to the Shadow Chronicles 1: The Enemy Within")
Over the period of a year, the REF refitted its fleet with new Shadow technology in preparation to launch an assault against Edwards and his ally, the Invid Regent. These new developments included the Shadow device, which hide all protoculture emissions; Synchro cannons, a powerful weapon similar to reflex cannons; and the Neutron-S missiles. (comic: "Robotech: Prelude to the Shadow Chronicles 1: The Enemy Within ")
This technology seemingly proved its worth when the REF was able to overwhelm Edwards and his Invid thralls. With this success, the REF moved to try to replicate it with a full scale assault on the Invid Regess' forces holding Earth. (comic: "Robotech: Prelude to the Shadow Chronicles 5: The Children of the Shadows")
Unbeknownst to the REF, the Haydonites were the true masters behind Shadow technology and had helped them "develop" the technology as part of an elaborate scheme to destroy them. They had hoped that the REF would blindly use the Neutron-S missiles to not only destroy the Invid, but themselves as well. Though this did not eventuate, the Haydonites knew the secrets of Shadow technology and turned the technology against its users, easily managing to overwhelm the REF fleet defending Space Station Liberty. (Robotech: The Shadow Chronicles)