Feedback Stabilization of Incompressible Flows using the Quadratic Constraint Framework*

Flow instabilities can create high shear regions that are detrimental to the performance of engineering systems. In this talk, we propose a framework to synthesize globally stabilizing feedback controllers to suppress such instabilities. The framework exploits the fact that the nonlinearity in the incompressible Navier-Stokes equations (NSE) is energy conserving. This property is expressed as a quadratic constraint and juxtaposed with the linear dynamics of NSE for controller synthesis using semi-definite programming (SDP). The resulting framework can be used to design full-state and static-output feedback controllers that stabilize the flow regardless of the perturbation magnitude.  We demonstrate the approach on a reduced-order model of plane Couette flow with body force actuation.