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