Line a rimmed baking sheet with parchment and spray the paper with nonstick cooking spray. In a medium saucepan, combine the sugar, corn syrup and water and bring to a boil over moderately high heat. Cook undisturbed until a deep-amber caramel forms, about 7 minutes. Remove from the heat. Stir in the rice cereal, banana chips, peanuts and baking soda.
Quickly spread the brittle on the baking sheet, separating it into pieces as much as possible with a spatula. Let cool until hardened, about 45 minutes. Coarsely chop the brittle or break it into clusters and serve.
The brittle can be stored in an airtight container for up to 3 days.