Web Request comes from same OS?

I want to make auto login on my web site. I don't want to ask username and password every time if user on the same machine and same browser.

On mobile devices I can do this but on browser I frozed. How can I understand securely on server side that request comes from same machine and browser ?

I don't want to set cookie with 1 year or greater valid. I think this will cause security issues.

Any advice ?

Best regards.