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.　(c)　2018　Optical　Society　of　America　under　the　terms　of　the　OSA　Open　Access　Publishing　Agreement