  This paper describes a robust linear time-invariant output-feedback control
strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in
wall-bounded turbulent fluid flows, that nonetheless gives performance
guarantees in the nonlinear turbulent regime. The novel strategy is effective
in reducing the supply of available energy to feed the turbulent fluctuations,
expressed as reducing a bound on the supply rate to a quadratic storage
function. The nonlinearity present in the equations that govern the dynamics of
the flow is known to be passive and can be considered as a feedback forcing to
the linearised dynamics (a Lur'e decomposition). Therefore, one is only
required to control the linear dynamics in order to make the system close to
passive. The ten most energy-producing spatial modes of a turbulent channel
flow were identified. Passivity-based controllers were then generated to
control these modes. The controllers require measurements of streamwise and
spanwise wall-shear stress, and they actuate via wall transpiration. Nonlinear
direct numerical simulations demonstrated that these controllers were capable
of significantly reducing the turbulent energy and skin-friction drag of the
flow.
