Most real-world fluid flows around aircraft, ground vehicles and water craft are predominantly turbulent. It is well-known that turbulent flows induce much higher skin-friction drag relative to laminar flows. For streamlined bodies such as ships and passenger aircraft, skin-friction drag can be the main contributor to the total drag on those vehicles. In this thesis, two different linear time-invariant output-feedback control methods will be investigated which aim to reduce skin-friction drag in turbulent wall-bounded flow. Both methods use wall-based sensing and actuation arrangements, and are evaluated upon direct numerical simulations (DNS) of turbulent channel flow. Spectral discretisation is used to produce highly accurate linear control models which are derived from the governing equations. The open-source DNS code used in the current work is outlined, and a procedure for modifying the boundary conditions at the walls is presented. The first control methodology investigated, passivity-based control, inhibits the ability of the flow to produce energy. Passive systems can only store and dissipate energy. It is shown how the nonlinear dynamics in the equations that govern turbulent flows are passive, and can be considered as a feedback forcing to the linearised dynamics. The linear spatial modes of the flow which are capable of producing the most energy are identified. Controllers are then developed which make these modes closer to passive, resulting in restricted turbulent energy production, and consequently, reduced skin-friction drag. H-infinity loop-shaping control is also investigated as a means of reducing turbulent skin-friction drag. This method offers a priori guarantees of closed-loop robustness to uncertainty and performance in terms of input disturbance rejection. Controllers are synthesised with the objective of minimising perturbation streamwise wall-shear stress in turbulent channel flow. It is shown that when enough spatial modes of a flow are controlled using this method, significant reductions in skin-friction drag can be achieved.