中文摘要：

基于鲁棒控制理论，研究了闭环供应链网络中企业间协同控制方法．采用差分方程描述了基于再制造的逆向物流过程；采用矩阵状态方程建立了双链组成的闭环供应链网络动态模型；提出了需求波动最差条件下，两个单链组成闭环供应链网络中节点企业协同运作的鲁棒Hx控制方法；采用l2范数方法量化了系统中的牛鞭效应；通过仿真实验观察牛鞭效应的抑制效果，验证了该方法的可行性．这一结果为闭环供应链网络的稳定性和节点企业的协同控制研究，提供了一种新的方法．

英文摘要：

Based on the robust control theory, the cooperation control methods between node companies in a closed - loop supply chain （CLSC） networks are studied. With the inventory, state difference equations, the inverse logistics process are described; and with the matrix state equations, the models of CLSC networks including two chains are established; In the worst case of the demand fluctuation, the robust Hx control methods for the cooperation operation between the node companies in the CLSC networks including two chains are presented. An 12 norm is described as a method to quantify the bullwhip effect in the system. By an ex- ample, the restrain impact of the bullwhip effect is observed in order to prove the methods feasibility. As a result, it presents a new method to study the system stability and the cooperation control methods among node companies in the networks including many closed-loop supply chains