Data-based control design for output-error linear discrete-time systems with probabilistic stability guarantees

In this letter we propose a novel method for direct data-based design of an output feedback controller for output-error processes in the single-input-single-output case. We consider a finite number of input/output data points collected from the system. Based on them, we define a set of state-space perturbed models consistent with data, where a bound on the disturbance is obtained by scenario optimization, and the structural properties of the models in this set are theoretically analyzed. This leads to a linear matrix inequality for the design of the feedback control law with probabilistic asymptotic stability guarantees. A simulated non-minimum phase system illustrates the approach.