Data-Driven Quadratic Stabilization of Continuous LTI Systems

Abstract This paper introduces a simple data-driven quadratic stabilization control (DDQSC) method to design a state feedback controller based solely on experimental measurements while avoiding explicitly identifying the plant. Rather, we seek a controller guaranteed to quadratically stabilize all plants that could have possibly generated the observed data. While in principle this leads to a very challenging non-convex robust optimization problem, our main result provides a convex, albeit infinite-dimensional, necessary and sufficient condition for the existence of such a controller and its associated Lyapunov function. In the second part of the paper, we provide a tractable finite-dimensional convex relaxation of this condition and illustrate its effectiveness with several examples.