###### Abstract  
As the market environment becomes increasingly complex, the demands for supply chain performance and security are continuously rising. Consequently, it is crucial to consider the role of trust factors within the system. This paper introduces a trust mechanism in the interaction between supply and demand within supply chain logistics and information flow. The supply chain system, characterized by varying degrees of trust, is modeled as multiple subsystems using the T-S fuzzy model. The challenge of mitigating the bullwhy effect, which refers to the amplification of demand variability within the supply chain, is reformulated as an \(H_{\infty}\) consistency problem. A productivity and distributed consistency protocol switching controller based on fuzzy rules is designed, providing sufficient conditions for the entire system to achieve consistency. The proposed method effectively suppresses the bullwhy effect and allows certain nodes in the system to be temporarily in an abnormal state. Finally, the method's effectiveness is validated through simulation examples. s [EMAIL_ADDRESS] 2024 14 1204  
of trust and to dynamically regulate the system according to trust values. Therefore, it is reasonable to construct a supply chain system model that incorporates a trust mechanism and to design a controller to regulate the system state based on trust information. Inventory state control is a crucial aspect of supply chain management. The main goal is to minimize inventory costs while meeting user demand, and incorporating trust factors in the supply and demand chain can enhance efficiency and stability. In recent years, researchers have conducted numerous studies on inventory management and performance optimization of supply chain systems using multi-agent systems (see [16; 17; 18; 19; 20; 21; 22]). For instance, ref. [17] discussed the utilization of an integrated procurement-production-inventory model to enhance company performance and reduce costs. Ref. [18] explored how machine learning techniques can strengthen the sustainability of the supply chain and optimize logistics and inventory management. Ref. [22] considered the management of inventory under dynamic demand and stochastic time scales. In the field of supply chain inventory system management, few scholars have focused on the stability and robustness of the system. However, the stability and performance of the system are significantly impacted by continuous interference from uncertainty factors and unexpected events. Control theory provides a framework for achieving stability through systematic thinking, whether globally or locally. The supply chain system is dynamic, and its stability and response time are seriously affected by uncertainties. Therefore, integrating control theory with supply chain inventory management is effective and logical. It is reasonable to propose a dynamic multi-agent supply chain model based on a trust mechanism, combined with control theory. To incorporate the concept of trust value into the supply chain system, this paper employs a fuzzy model to integrate trust value information with the supply chain model. The Takagi-Sugeno (T-S) fuzzy model is significant in the field of system modeling and control, offering unique advantages for handling complex, nonlinear systems (see [23; 24; 25]). Consequently, this paper constructs a productivity and distributed consensus protocol controller based on fuzzy rules derived from the T-S fuzzy model. There are various methods for assessing supply chain performance, including (1) total supply chain cost, (2) service level, (3) average inventory, and (4) the bullwhip effect, among others. Among these performance assessment procedures, we focus on the bullwhip effect because it is a critical area of applied research in supply chain management [26]. Market demand can fluctuate due to factors such as customer satisfaction, product reliability, and the economic environment.