In the present work, a simple proportional feedback control is designed to suppress the
vortex-shedding instability in the wake of a prototype bluff-body flow, i.e., the flow around a square
cylinder confined in a channel with an incoming Poiseuille flow. Actuation is provided by two jets
localized on the cylinder surface and velocity sensors are used for feedback control. This particular
configuration is a pretext to propose a more general strategy for designing a controller, which is
independent of the type of actuation and sensors. The method is based on the linear stability analysis
of the flow, carried out on the unstable steady solution of the equations, which is also the target flow
of the control. The idea is to use sensitivity analysis to predict the displacement in the complex plane
of some selected eigenvalues, found by the linear stability analysis of the flow, as a function of the
control design parameters. In this paper, it is shown that the information provided by only sensitivity
analysis carried out on the uncontrolled system is not sufficient to design a controller which
stabilizes the flow. Therefore, the control is designed iteratively by successive linearizations. Apart
from possible constraints, the position of the sensors, the direction along which velocity is
measured, and the feedback coefficients are outputs of the design procedure. The proposed strategy
leads to a successful control up to a Reynolds number which is at least twice as large as the critical
one for the primary instability, using only one velocity sensor