  In this article, we propose a Lyapunov stability approach to analyze the
convergence of the density operator of a quantum system. In analog to the
classical probability measure for Markovian processes, we show that the set of
invariant density operators is both closed and convex. We then show how to
analyze the stability of this set via a candidate Lyapunov operator. We
complete our analysis of the set of invariant density operators by introducing
an analog of the Barbashin-Krasovskii-La Salle theorem on the dynamics of
quantum systems.
