Tug Driver reported while pushing Lear 45 into hangar with one wing walker on the left wing; the right winglet made contact with a parked tug.

Narrative

While pushing back the aircraft into the hangar contact was made with another tug damaging the right side winglet. Impacted right wingtip on the King Air tug while pushing into the hangar. Being on night shift I had a good days sleep and eaten a proper dinner. I monitored the departure time from ZZZ to arrive and meet the aircraft. When the aircraft arrived I opened the hangar door and positioned the tug for push back. The operating crew attached the tug and I commenced the push. I had a wing walker on the right side to monitor the hangar wall as that is the critical side due to the longer wingspan. The King Air was not in the hangar so there was plenty of maneuvering space. Even though I was monitoring both sides my focus was on the right side. I looked to the left and realized the conflict with the king air tug just as it touched. I immediately stop the motion on the tug and examined the Lear wingtip and realized I had caused damage. I reported this to the inbound PIC. My apologies for this situation. What could have prevented this from occurring would have been more proactive on having additional wing walkers. A step back and a critical assessment of the hangar environment for potential hazards prior to any movement. An additional risk is possible complacency by all from having pushed before when additional personnel were not always available. I would also recommend that as a practice that all tugs be positioned away from the floor and parked along the wall when not in active use. I do accept full responsibility for this incident as I was the driver of the tug