The outer corners of my eye's are saggy, which make me look tired all the time. Are there procedures that can fix this? (photo)

From your photograph the position of the corner of your eyes, the canthal area looks normal and is not drooping.  The normal position to lift a sagging eye is a canthoplasty.  However as others have stated you do have a slight lid droop called ptosis which may be contributing to your looking tired.  Please consult a board certified plastic surgeon who is experienced an oculoplastic surgery.

Ptosis surgery is what is likely to make you better.  Find a fellowship trained oculoplastic surgeon for this procedure.  Do not settle on just any surgeon.  You need someone who is specially trained.  The American Society for Ophthalmic Plastic and Reconstructive Surgery maintains a geographic directory on its website (ASOPRS dot org) that includes international listings.  

You have mild upper eyelid Ptosis [droopy eyelid] that can make people look tired or sleepy. The outer corners of your eye [lateral canthus] seems in a relatively normal position. Changing that anatomy [canthoplasty/canthopexy] is very rarely natural looking, so I would recommend against changing that. A mild ptosis repair may give you exactly what you are looking for. I have posted a photo of a young lady with the same concern and the surgical outcome.