I remember reading a series of books in the early 90s (at least 4, maybe as many as 6) that were set on and around a future Earth where vast cities covered the planet. There was a grimy underground habitat where poor, exiled and fugitive people worked, and some of the ultra rich lived in orbiting space stations. There was a rigid class structure and ruling families, and I think the Chinese were the dominant race.
Can anyone help me track this down? I don't have the books, can't remember the author, and can't craft a Google search that helps. If it matters, I lived in England back then and the books were readily available from good bookstores, if not prominently advertised or displayed. I can't remember whether it was an ongoing or finished series.