  Based on a continuum theory, we investigate the manipulation of the
non-equilibrium behavior of a sheared liquid crystal via closed-loop feedback
control. Our goal is to stabilize a specific dynamical state, that is, the
stationary "flow-alignment", under conditions where the uncontrolled system
displays oscillatory director dynamics with in-plane symmetry. To this end we
employ time-delayed feedback control (TDFC), where the equation of motion for
the ith component, q_i(t), of the order parameter tensor is supplemented by a
control term involving the difference q_i(t)-q_i(t-\tau). In this diagonal
scheme, \tau is the delay time. We demonstrate that the TDFC method
successfully stabilizes flow alignment for suitable values of the control
strength, K, and \tau; these values are determined by solving an exact
eigenvalue equation. Moreover, our results show that only small values of K are
needed when the system is sheared from an isotropic equilibrium state, contrary
to the case where the equilibrium state is nematic.
