You can use preg_replace like this to archive desired result:
preg_replace('/(<link\b.+href=")(?!http)([^"]*)(".*>)/', '$1'.$url.'$2$3$4', $html);
So this code (assuming is stored in $html and $url = 'http://mydomain.com/'):
<link rel="stylesheet" href="style.css" type="text/css">
<link rel="stylesheet" href="style2.css" type="text/css">
<link rel="stylesheet" href="http://google.com/style3.css" type="text/css">
<link rel="stylesheet" href="style4.css" type="text/css">
<link rel="stylesheet" href="https://google.com/style5.css" type="text/css">
<link rel="stylesheet" href="some/path/to/style6.css" type="text/css">
Will be converted to this:
<link rel="stylesheet" href="http://mydomain.com/style.css" type="text/css">
<link rel="stylesheet" href="http://mydomain.com/style2.css" type="text/css">
<link rel="stylesheet" href="http://google.com/style3.css" type="text/css">
<link rel="stylesheet" href="http://mydomain.com/style4.css" type="text/css">
<link rel="stylesheet" href="https://google.com/style5.css" type="text/css">
<link rel="stylesheet" href="http://mydomain.com/some/path/to/style6.css" type="text/css">