Feedback Stabilization of a Boundary Layer Equation. Part 2: Nonhomogeneous State Equations and Numerical Simulations

We study the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of known perturbations. The feedback law is determined by solving a Linear-Quadratic optimal control problem. The observation is the laminar-to-turbulent transition location linearized about its stationary position, the control is a suction velocity through a small slot in the plate, the state equation is the linearized Crocco equation about its stationary solution. This article is the continuation of [7] where we have studied the corresponding Linear-Quadratic control problem in the absence of perturbations. The solution to the algebraic Riccati equation determined in [7], together with the solution of an evolution equation taking into account the nonhomogeneous perturbations in the model, are used to define the feedback control law.