The easiest solution would be to fix a diagonal tension/compression member across the back, from the top left corner to the bottom right corner. If you use a rigid support like a metal rod, you'll just need one. If you use something like steel cable or webbing, you'll need two forming an X. Note that whatever you use cannot have much stretch to it, or the wardrobe will be wobbly even if it isn't in danger of falling down.

An eye bolt at each end with a turnbuckle in the middle would be a good solution for getting steel cables taut.

The easiest solution would be to fix a diagonal tension/compression member across the back, from the top left corner to the bottom right corner. If you use a rigid support like a metal rod, you'll just need one. If you use something like steel cable or webbing, you'll need two forming an X. Note that whatever you use cannot have much stretch to it, or the wardrobe will be wobbly even if it isn't in danger of falling down.

An eye bolt at each end with a turnbuckle in the middle would be a good solution for getting steel cables taut. Use crimping sleeves to hold everything in place, and cable thimbles for the bends to reduce stress on the cable.