"Madman" is shorthand for "Putin sits at the apex of a rigid, hierarchal system that tolerates no signs of weakness from the top, and has invested far too much personal political capital into this war, so he won't back down almost no matter what happens on the ground."
I suppose a certifiable madman would have flung nukes by now. Hopefully he never does that. Regardless, what Putin perceives to be in his own short-term political interests is indeed madness for his country, and for the world.
I've heard it opined that this war won't end while Putin is alive. That seems a fair assessment. Unless more fuel gets poured on the fire in the form of Russian mass conscription or WMDs, perhaps this war is settling toward a frozen, lower-level conflict similar to what has already existed in the Donbas region since 2014.
Is that state of affairs sustainable? Well, evidently it is - as it's already proven "sustainable" for 8 years. The Israel-Palestine conflict has been simmering for decades. Many post-colonial conflicts in Africa - same.