Abuse of power = allude her death by the blade running along her throat. Creates a sinister tone that he has absolute power over everything and can dispose her and all. Duke is irritated by the blush as she is his.
'I gave a command ; Then all smiles stopped together.'
Exudes pride over power = The Duke glosses over the nature of his commands which ends the Duchess. It tells us her freedom was stripped away from her and now obeys the Duke. The caesura further emphasises the blatant stop to the Duchess' happiness.
'That's my last Duchess painted on the wall'
Inequalities affect women = Her portrait is a trophy and symbol of the power he wields over his wife. 'That' implies he sees her as an object which she literally is now. She has been reduced to art for the male gaze, feminist concept presenting the dehumanisation as she is only viewed for beauty. 'painted' could be the Dukes belief she was a harlot painting her face = often done by whores
'a gift of a nine-hundred-years-old name'
Power in wrong hands = symbolic of the family's long standing wealth and status. He doesn't count love and affection as part of the deal but she should be tamed through marriage.
Form = dramatic monologue, The Duke is speaking to a silent listener the envoi for his wife's father. This tells us he power and control the Duke as as its one sided and we never hear from the wife.
Structure = One long stanza, The Duke is unable to control his thoughts and feelings as he blurts out the speech, this is also backed up by enjambment as everything is uncontrolled and he does not have the power he thinks he has
