In this paper, the leader-following consensus problem for discrete-time nonlinear multi-agent systems with delay and parameter uncertainty is investigated, with the objective of designing an output feedback protocol such that the multi-agent system achieves leader-following consensus and has a prescribed performance level. By model transforming, the leader-following consensus control problem is converted into robust control problem. Based on the Lyapunov function technology and the linear matrix inequality method, some new sufficient conditions are derived to guarantee the consensus of discrete-time nonlinear multi-agent systems. The feedback gain matrix and the optimal performance index are obtained in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.
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