LMI-Based H-infinity Control of CLSC Networks with the Third Party Reverse Provider

Based on linear matrix inequality(LMI), the operation of the closed-loop supply chain(CLSC) networks with the third party reverse providers (3PRLP) are studied. The model of CLSC networks is established. An l2 norm of the discrete-time transfer function of CLSC networks is described as a method to quantify the bullwhip effect. It is the minimum of the up bounded of the bullwhip effect. To reduce the bullwhip effect, we apply LMI approach to design a H∞ control strategy in the worst case that the end customer´s demand is the most fluctuation. To prove it, we give a number example. As a result, it presents a new method to study the stability of CLSC networks and restrain their bullwhip effects.