Data-based Transfer Stabilization in Linear Systems

We present a novel framework for transferring the knowledge from one system (source) to design a stabilizing controller for a second system (target). Our motivation stems from the hypothesis that abundant data can be collected from the source system, whereas the data from the target system is scarce. We consider both cases where data collected from the source system is noiseless and noisy. For each case, by leveraging the data collected from the source system and a priori knowledge on the maximum distance of the two systems, we find a suitable, and relatively small, compact set of systems that contains the actual target system, and then provide a controller that stabilizes the compact set. In particular, the controller can be obtained by solving a set of linear matrix inequalities (LMIs). Feasibility of those LMIs is discussed in details. We complement our theoretical findings by two numerical case studies of low-order and high-order systems.