With the advancement of multi-agent systems control theory, its applications in intelligent transportation, unmanned aerial vehicle swarms, and other engineering domains have become increasingly prominent. Among various control approaches, sampled-data control has emerged as a key research direction due to its strong alignment with practical engineering requirements. However, in real-world scenarios, agents often operate under multiple constraints, such as non-convex velocity and control input constraints, which not only introduce strong nonlinear characteristics in the system but also significantly increase the complexity of control law design. To address these challenges, this thesis investigates consensus control for constrained multi-agent systems within a sampled-data framework. A distributed consensus control algorithm is proposed for multi-agent systems with non-convex velocity and control input constraints under sampled-data dynamics. First, a model transformation technique is employed to convert the original constrained system into an equivalent unconstrained linear system, effectively mitigating the strong nonlinearities introduced by the non-convex constraints. Second, by leveraging the stochastic matrix analysis method, an iterative process is constructed to characterize the evolution of system states. Utilizing the properties of stochastic matrices, it is rigorously proven that all agents achieve consensus under non-convex constraints. Finally, numerical simulations are conducted to further verify the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.