You should definitely start by reading Ten Days in a Mad-House, the expose by undercover investigative journalist Nellie Bly from 1887.

As for secondary scholarship, it usually helps to be more specific about what you are looking for with search terms--for example, looking up something like "history autism institutionalization" will get better results than "insane asylum nineteenth century" or some such.

I recently read Robert Hornick, The Girls and Boys of Belchertown, which is about a specific state institution/school for developmentally disabled children that opened in the early 20th century. It has a nice retrospective on 19th century philosophies of management/treatment in one of the earlier chapters as well.