In a "Rose for Emily," how does Homer Barron have control over Emily?
Since Homer is Emily's first beau, I think he exerts a great deal of control over her, probably much like her father controlled her. She meets him the summer after her father's death, and she realizes her life will have no meaning without a husband. She's willing to risk her reputation by being seen in public with him on their buggy rides, and she stands up to her cousins when they visit her to talk about Homer. In effect, Emily gives up everything to be with Homer. When he leaves town, I think Emily panics at the thought of losing him. She knows she can't shame him into marrying her, since he's a Yankee and doesn't have the same Southern values that Emily has been raised with. So Emily does the only thing she can to keep him with her forever.
Emily's father chased away all of her suitors, and she is fearful of being a spinster. Homer asserts that he is not a marrying man to some of the townspeople, but Emily holds on desperately to what she fears will be her last chance to marry.
The desperation of her decision to kill him shows the hold he had on her. Emily was so afraid he would leave her, she killed him to keep him in her life.