Ecosystem respiration (Reco) represents a major component of the global carbon cycle, and accurate characterization of its dynamics is essential for a comprehensive understanding of ecosystem-climate interactions and the impacts of climate extremes. This paper presents a novel data-driven and physics-aware method for estimating Reco dynamics using the dynamic mode decomposition with control input (DMDc) technique. The proposed model represents Reco as a linear dynamical system with an autonomous component and an exogenous control input, such as air temperature (Tair), or other observed drivers, such as soil temperature and/or soil water content. This unique modeling approach allows controlled intervention to study the effects of different inputs on the system. Experimental results using Fluxnet2015 data show that the prediction accuracy of Reco dynamics achieved with DMDc is comparable to state-of-the-art methods, making it a promising tool for analyzing the dynamic behavior of different vegetation ecosystems in response to climate change.