Local Stabilization of Navier-Stokes systems via Observer-Based Feedback

Maintaining laminar flow and reducing drag is important from a turbulence engineering perspective. Much of the existing work on the stabilization control problem for stationary solutions modeled by the Navier-Stokes equation is based on state feedback. Our previous work has proposed a stabilization method for a linear distribution parameter system of parabolic type based on observer-based feedback, and the model of the system corresponds to the linear approximation problem of the Navier-Stokes flow stabilization problem. In this paper, we show that a nonlinear system applicable to the Navier-Stokes system can be stabilized by using the linear controller proposed in the previous work if the state is sufficiently close to the stationary solution with respect to a seminorm. This design method has also been successful in suppressing control and observation spillovers.