Data-driven output feedback control of nonlinear systems: Stabilization and robustness

In this article, we introduce a method to deal with the data-driven control design of nonlinear systems from input-output data only. We derive conditions to design dynamic output feedback controllers that render the closed-loop system dominantly linear using a growth condition on basis functions. These conditions take the compact form of data-dependent linear matrix inequalities. The method returns controllers that can be certified to stabilize the system even when the input-output data are perturbed. We extend the method to tackle neglected nonlinearities. Results are illustrated with numerical examples.