On a Distributed Control Law with an Application to the Control of Unsteady Flow around a Cylinder

A new class of feedback laws for distributed control of dynamical systems is presented. The approach is based on instantaneous control, i.e. control at every time step to the underlying dynamical system. The closed-loop controllers obtained in this way can be proved to be stable in the distributed control case for dynamical systems in finite dimensions, provided that the parameters of the controller are suitably adjusted [4]. As an application a distributed controller for the unsteady flow around a cylinder is numerically investigated. As the numerical results show the approach presented is capable of stabilizing systems with very large dimensions.