Data Informativity for Stabilization of Discrete-Time Infinite-Dimensional Systems

Abstract

Abstract. This paper develops a framework for data-driven stabilization of discrete-time infinite-dimensional systems. We investigate informativity for stabilization, defined as the existence of a state-feedback gain that stabilizes all systems consistent with the available input-state data. Assuming that infinite-length data are Bessel sequences, we first establish a sufficient condition for data informativity in the noise-free case. We next show that this sufficient condition is also necessary under a mild data assumption when the input space is one-dimensional. Furthermore, if the state sequence forms a frame, then the sufficient condition can be extended to the case of noisy data. Finally, when the unstable part of the true system is known to be finite-dimensional, we derive a necessary and sufficient condition for informativity of finite-length data.