  Based on Lyapunov control theory in closed and open systems, we propose a
scheme to generate W state of many distant atoms in the cavity-fiber-cavity
system. In the closed system, the W state is generated successfully even when
the coupling strength between the cavity and fiber is extremely weak. In the
presence of atomic spontaneous emission or cavity and fiber decay, the
photon-measurement and quantum feedback approaches are proposed to improve the
fidelity, which enable efficient generation of high-fidelity W state in the
case of large dissipation. Furthermore, the time-optimal Lyapunov control is
investigated to shorten the evolution time and improve the fidelity in open
systems.
