  The problems of nonlinearity and high dimension have so far prevented a
complete solution of the control of turbulent flow. Addressing the problem of
nonlinearity, we propose a flow control strategy which ensures that the energy
of any perturbation to the target profile decays monotonically. The
controller's estimate of the flow state is similarly guaranteed to converge to
the true value. We present a one-time off-line synthesis procedure, which
generalises to accommodate more restrictive actuation and sensing arrangements,
with conditions for existence for the controller given in this case. The
control is tested in turbulent channel flow ($Re_\tau=100$) using full-domain
sensing and actuation on the wall-normal velocity. Concentrated at the point of
maximum inflection in the mean profile, the control directly counters the
supply of turbulence energy arising from the interaction of the wall-normal
perturbations with the flow shear. It is found that the control is only
required for the larger-scale motions, specifically those above the scale of
the mean streak spacing. Minimal control effort is required once laminar flow
is achieved. The response of the near-wall flow is examined in detail, with
particular emphasis on the pressure and wall-normal velocity fields, in the
context of Landahl's theory of sheared turbulence.
