They look burnt, how close are the lights to the leaves? Better pictures of the entire plant and the pot will be a big help determining what is going on. When i bring mine in I put her as close as I can to a south facing window and reduce watering by half, some leaves will die back but not like yours are doing. If it is pot bound you really need to wait til late Spring to pot up.

Wow, your plant is slowly dying. Try giving it some water and fertilizer.

Sorry to contradict you Dave, but giving a plant that is stressed fertilizer now will not help it at all.

Vladimir, I dig mine, cutting off all but the last emerging leaf, and take them into an unheated shop. There they overwinter and are then replanted in the spring. Easier than trying to keep them growing after a huge change in light levels.

Check your soil, is it wet or dry? check that the drain holes in your pots are clear and open. Usually they don't grow much in the winter. So don't need as much water. Humidity levels can effect bananas as well, I would cut off the dead/dying leaves, (leaving the last leaf it produced), and move the light back away from it some.

Being pot bound should not cause that sort of damage.

I don't think the leaves are just drying up... they first turn yellowy brown and shrivel and than dry up. It's as if the plant is feeding off it's own leaves to save the main plant. My banana plant is inside a basement with some light coming from the windows and the same thing happened to the lower, older leaves. All the others towards the top is a healthy green and the plant is putting out a leaf a month. I gave my plant some water and fertilizer.