Can pets read human emotions?

I believe pets can sense our emotional state. My cat seems to know when I'm unhappy or in pain and tries to comfort me. She usually snuggles near my head and tried to groom my forehead. She even has gone to get other family members and led them to my room, wanting them to check on me.

She also is bossy and went it gets to be getting into the week hours of the morning, she is relentless in her complaints to get me to go to bed.