Data-Driven Control of Discrete-Time Two-Dimensional Systems With Noisy Data

This paper considers the stabilization issue of unknown two-dimensional (2-D) Fornasini–Marchesini (FM) systems with noisy data. Note that existing results on 2-D systems require accurate system models, which are almost impossible to be obtained in practice. Within this context, a robust data-based control strategy for unknown 2-D FM systems is put forward herein. First, based on the data collection of 2-D input and state measurements, the data-based representation is established for a set of 2-D FM systems consistent with these sampled data, leading to the purpose of stabilizing such a set of data-consistent 2-D dynamics with robustness. Then, the noisy data embedded in the set of data-consistent 2-D dynamics is expressed by virtue of a matrix ellipsoid, which motivates the potential of applying Petersen's lemma to cope with the noise impacts in the closed loop. Next, data-driven sufficient conditions on ensuring the stability of 2-D FM systems are developed, and the feasibility of such convex programming leads to the control strategy synthesis with data informativity. Finally, the effectiveness and applicability of the developed data-based 2-D control scheme are verified by the case study of the Darboux equation.