  Transient energy growth of flow perturbations is an important mechanism for
laminar-to-turbulent transition that can be mitigated with feedback control.
Linear quadratic optimal control strategies have shown some success in reducing
transient energy growth and suppressing transition, but acceptable worst-case
performance can be difficult to achieve using sensor-based output feedback
control. In this study, we investigate static output feedback controllers for
reducing transient energy growth of flow perturbations within linear and
nonlinear simulations of a sub-critical channel flow. A static output feedback
linear quadratic regulator~(SOF-LQR) is designed to reduce the worst-case
transient energy growth due to flow perturbations. The controller directly uses
wall-based measurements to optimally regulate the flow with wall-normal blowing
and suction from the upper and lower channel walls. Optimal static output
feedback gains are computed using a modified Anderson-Moore algorithm that
accelerates the iterative solution of the synthesis problem by leveraging
Armijo-type adaptations. We show that SOF-LQR controllers can reduce the
worst-case transient energy growth due to flow perturbations. Our results also
indicate that SOF-LQR controllers exhibit robustness to Reynolds number
variations. Further, direct numerical simulations show that the designed
SOF-LQR controllers increase laminar-to-turbulent transition thresholds under
streamwise disturbances and delay transition under spanwise disturbances. The
results of this study highlight the advantages of SOF-LQR controllers and
create opportunities for realizing improved transition control strategies in
the future.
