In this paper,the control of complex delayed networks with different nodes is proposed.Firstly,the stabilization of coupled networks with time delay is investigated.By constructing a Lyapunov function,a linear feedback controller design procedure for the networks is converted to the problem of solving a set of linear matrix inequalities.Then the results are extended to networks with both delayed dynamical nodes and delayed couplings.It is shown that the stabilization of complex networks is determined by the dynamics of each uncoupled node,coupling matrix and feedback gain matrix of networks.Two examples are simulated.In the first example,a network with 10 nodes consisting of Lorenz systems and systems proposed by Zhang in 2009 is given.It is found that the network states are divergent without control,and convergent under designed linear feedback controllers.In the second example,a larger network with 100 nodes consisting of delayed Chen systems and delayed Lorenz systems is given.The proposed method is also effective for large scale networks.
The buyer-supplier relationship plays a great role in most economic systems. The buying firm usually tries to find a new supplier who provides products with satisfying quality and lower price. A broad branch of literature deals with the development of buyer-supplier relationships, but limited research is on the circumstances under which a buyer should terminate such a relationship and switch to a new supplier. In this paper, the incentive compatibility constraint (IC) which induces the entrant supplier to report his true cost is considered, and the participation constraint (PC) which ensures the entrant supplier to get at least reservation profit is taken into account. Then the supplier switching model is set up to minimize the buying firm's total procurement cost which includes the transfer payment to the incumbent supplier, the payment to the entrant supplier and the switching cost, and the buying firm's switching cost is considered as a function of the switching quantity. With the theoretical analysis of IC, PC and the proposed model, the optimal supplier switching strategy can be obtained. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the switching strategy.
