  We characterize the dynamical behavior of continuous-time, Markovian quantum
systems with respect to a subsystem of interest. Markovian dynamics describes a
wide class of open quantum systems of relevance to quantum information
processing, subsystem encodings offering a general pathway to faithfully
represent quantum information. We provide explicit linear-algebraic
characterizations of the notion of invariant and noiseless subsystem for
Markovian master equations, under different robustness assumptions for
model-parameter and initial-state variations. The stronger concept of an
attractive quantum subsystem is introduced, and sufficient existence conditions
are identified based on Lyapunov's stability techniques. As a main control
application, we address the potential of output-feedback Markovian control
strategies for quantum pure state-stabilization and noiseless-subspace
generation. In particular, explicit results for the synthesis of stabilizing
semigroups and noiseless subspaces in finite-dimensional Markovian systems are
obtained.
