Global observer design for Navier-Stokes equations in 2D

We consider Navier-Stokes equations on a rectangle with periodic boundary conditions, and known input. Given continuous measurements as averages of NSE’ solution over a set of squares we design a globally converging observer for NSE by relying upon Lyapunov method: we propose a parametric LMI for determining observer’s gain and size of squares, required for the global convergence. We illustrate the numerical efficacy of our algorithm by applying it to estimate states of NSE with Kolmogorov forcing.