A novel Data-Driven representation of Linear Systems based on Dynamic Mode Decomposition with Control to deal with noisy data
In this paper, data generated by a plant that can be described as a linear time-invariant system subject to both process and measurement noise are considered. An original and structured organization of the collected input–output data is introduced, leading to an alternative representation of the system dynamics within an extended state-space framework. Based on this formulation, the Dynamic Mode Decomposition with Control algorithm is employed to identify a Data-Driven model in a lifted space. The resulting representation enhances robustness with respect to noise, allowing for a more accurate and reliable characterization of the underlying system dynamics in the presence of disturbances and measurement uncertainty. The proposed approach is assessed through numerical simulations, which illustrate its effectiveness in capturing the system behavior and mitigating the impact of noisy data, thereby highlighting its potential for data-driven modeling and control applications.