Hybrid components, monadically

In the specification of state-based components as (generalised) Mealy machines, the underlying behaviour model --- expressing e.g. partial, nondeterministic or probabilistic evolution --- can be nicely captured by a (strong) monad. A suitable component algebra is then developed on top of its Kleisli category. After summarising this framework, we show how continuous evolution, a major issue in the design of hybrid systems, can be encoded in a similar way and discuss the resulting component calculus.