On Persistency of Excitation and Formulas for Data-Driven Control

In a paper by Willems and coworkers it was shown that persistently exciting data could be used to represent the input-output trajectory of a linear system. Inspired by this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent Linear Matrix Inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state feedback stabilization and the linear quadratic regulation problems. We also extend the stabilization problem to the case of output feedback control design