  We define and study basic properties of *-continuous Kleene $\omega$-algebras
that involve a *-continuous Kleene algebra with a *-continuous action on a
semimodule and an infinite product operation that is also *-continuous. We show
that *-continuous Kleene $\omega$-algebras give rise to iteration
semiring-semimodule pairs. We show how our work can be applied to solve certain
energy problems for hybrid systems.
