On triangulated categories we have a notion of [Bridgeland stability conditions][1].

Is there any known notion of "derived stability conditions" on a stable $\infty$-category $C$ such that they become Bridgeland stability conditions after passing to the homotopy category $hC$?


  [1]: http://annals.math.princeton.edu/wp-content/uploads/annals-v166-n2-p01.pdf