Prep the fruit by peeling and slicing the bananas into rounds.
In a medium saucepan, combine the sugar and water.
Cook over low heat, stirring gently until the sugar has completely dissolved to create a simple syrup.
Add the grated ginger, lemon juice, and cinnamon sticks to the syrup. Increase the heat to medium and bring the mixture to a rolling boil.
Reduce the heat to low and allow the syrup to simmer for 5 minutes, infusing it with the warm, spicy flavors.
Stir in the dried tropical fruit and the sliced bananas. Return the mixture to a boil, then immediately reduce the heat to low, cover the saucepan, and let it cook at a gentle simmer until the dried fruit is plump and tender.
Remove the compote from the heat and carefully fish out the cinnamon sticks. You can serve it immediately while it's warm, or let it cool and refrigerate overnight to serve chilled.
Don't be afraid to mix and match your dried fruits. Dried apricots, figs, or cherries would also be delicious additions to the tropical blend.