Feedback control for quadratic nonlinear systems

We propose two state feedback control strategies based on quadratic stability for quadratic nonlinear systems, specifically reduced order fluid flow models. Stabilizing linear controllers are designed at each operating point, but unlike traditional linear designs, the nonlinear dynamics are taken into account during the design process by representing them as elements of a bounding set. By solving a set of linear matrix inequalities an estimate of the region of attraction at each operating point of the closed loop system is presented. The overall design consists of a sequence of linear controllers that regionally stabilize and enlarge the region of attraction of the desired operating points. Under the assumption that the system admits a centered-ε-cover, a switching strategy is proposed that achieves semiglobal stabilization of the nonlinear system.