In "My Last Duchess," a husband murders his wife because she blushes and smiles at other people – even though theses blushes are out of her control and probably entirely innocent. This is pretty much the textbook definition of an abusive, controlling husband. The Duke doesn’t even want his wife to thank people for gifts, because it makes him jealous. But we think this goes beyond abuse into the realm of madness: after all, trying to control someone is abuse; thinking that because someone blushes she must be having an affair, and that the only remedy is murder is just insane.
The Duke’s obsession with totalitarian power, and his tendency to punish innocent or nearly innocent behavior with the most extreme penalties, make it clear that he’s a psychopath.