LINEAR FEEDBACK CONTROL OF TRANSITION IN SHEAR FLOWS J´ erˆ ome Hœpffner 1 , Mattias Chevalier 1,2 , Thomas Bewley 3 , and Dan Henningson 1,2 1 Department of Mechanics, Royal Institute of Technology (KTH) SE-100 44 Stockholm, Sweden, 2 The Swedish Defense Research Agency (FOI), SE-172 90, Stockholm Sweden 3 Flow Control Lab, Dept of MAE, UC San Diego, La Jolla, CA 92093-0411, USA. Abstract This work focuses on the application of linear feedback control to tran- sition to turbulence in shear flows. The controller uses wall-mounted sensor information to estimate the flow disturbances and uses wall ac- tuators to prevent transition to turbulence. The flow disturbances are induced by external sources of perturbations described by means of a stochastic volume forcing. We show that improved performance can be achieved if the proper destabilisation mechanisms are targeted. Keywords: Feedback control, LQG, state estimation, Kalman filter, stochastic dis- turbance model. 1. Introduction In many applications like aeroplane wings, pipes, turbine blades, growth of small disturbances due to external sources of excitation can lead to transition to turbulence and thus increase the friction drag. Control is being increasingly applied to fluid flow as the theories and devices are being developed (see Bewley, 2001, Kim, 2003). A powerful theory for linear feedback control is available and can be applied to flow control, assuming a linear dynamics for the flow (small amplitude disturbances), with a quadratic objective function, and a Gaussian distribution for the external sources of excitation and measurement noise. This method known as LQG (Linear, Quadratic, Gaussian) or L 2 control (see Green and Limebeer, 1995) is used in this work. 2. System and control setup In this work, the dynamics of small perturbations to a laminar base flow is modelled by the linearized Navier–Stokes equation. Measure-