Add ID to widget within a dynamic sidebar

I would like my widgets to have a unique ID, preferably based on the title given to the widget. My specific case is that I would like to have a jump link (<a href="#widget-title">) to target widgets in a dynamic sidebar located in the footer of my site. I would like my widget to be wrapped in a div, i.e. <div id="widget-title">, or even better, if I could add that id to the tag that contains the widget’s title, i.e. <h3 id="widget-title"> (I’d love to avoid an extraneous div).

I know that each widget has its own ID somewhere that I could access, but I worry that if I use that, then add/change/delete widgets later, the ID may change. But I can and will always keep the widget title consistent. Right now the widget I have in mind has an ID of custom_html-4, but I’d like something more static and semantic.