Adding title to stylesheet link

This code from wp-includes/class.wp-styles.php:
is the code used to turn an attribute for the title into a title=”xxx” in the HTML code.

$title = isset($this->registered[$handle]->extra[‘title’]) ? “title='” . esc_attr( $this->registered[$handle]->extra[‘title’] ) . “‘” : ”;

How do I put the reference to populate that attribute from a theme?

I can’t find documentation on this, or anything clear about how ->registered or ->extra get controlled by a reference in a theme.

Any help or pointers would be appreciated.

– Mike