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In this paper, we study the cooperative control of linear, discrete-time multi-agent systems with fixed information structure and without communication delays. Based on the bilinear matrix inequality (BMI), the sufficient condition is obtained for the stabilization of multi-agent systems composed of N agents. Then, the design problems of cooperative controllers are converted into the optimization problems with BMI constraints. To solve these problems, an optimization algorithm is proposed. Finally, numerical examples are provided to demonstrate the reduced conservation of the proposed condition.