The uncertainty in hydrogen demand leads to a misalignment between the actual operation of the hydrogen supply chains and its expected planning, resulting in unnecessary resource waste and increased economic costs. To address this issue, a collaborative control strategy is proposed to coordinate multi-regional production-inventory operations in the hydrogen supply chains. Firstly, considering internal and external factors such as hydrogen storage losses and transportation delays, a dynamic mechanism model of the hydrogen supply chain operation is established. Then, aiming at the goal of multi-regional coordination under uncertain demand, the operational mechanism model is transformed into a state-space control model. Subsequently, based on Lyapunov-Krasovskii time-delay stability analysis and large-scale system control theory, the multi-regional coordination performance of the production-inventory control system is analyzed, and a control strategy is designed. Finally, a case study of a three-region hydrogen supply in a power system is presented to demonstrate the effectiveness of the proposed strategy. The results show that the collaborative control enables multi-regional production-inventory operations to align with expected planning. Compared to scenarios without collaborative control, the average deviation in hydrogen production and storage is reduced by 82.2%, effectively lowering operational costs. Thus, this study provides a decision-support solution for enterprises in the hydrogen supply chains.