When applying this data-driven control approach to real-world systems, several limitations and challenges may arise. One major limitation is the assumption of bounded noise in the data, which may not always hold in practical scenarios. Dealing with unbounded or time-varying noise can lead to inaccuracies in the identified system model and affect the performance of the controller. Moreover, the complexity of the system dynamics and the high dimensionality of the data can pose challenges in terms of computational efficiency and real-time implementation. Practical constraints such as actuator saturation, sensor noise, and communication delays also need to be considered in the control design to ensure stability and robustness of the system.