Abstract: In recent years, multiagent systems (MASs) have completed numerous complex tasks through effective communication and coordination among agents. This has enhanced MAS’s robustness and controllability, leading to their widespread application in practical scenarios such as spacecraft, robot, and unmanned aerial vehicle systems. MAS cooperative control, which includes addressing issues such as consistency, clustering, and formation, has garnered significant attention in the engineering field. This paper addresses the cooperative control problem of a nonlinear MAS affected by unknown control direction, unknown input constraints, and state time delay. We propose an adaptive fuzzy preset time control strategy to tackle these challenges. A preset time performance function ensures that the output error meets constraint requirements within a preset time, where the upper limit of the convergence time does not depend on the initial state of the systems and can be preset according to the actual demand. Therefore, this strategy offers more accurate convergence times compared with traditional finite-time and fixed-time control methods, thereby reducing control costs. State time delay, a common issue in many physical systems, often arises from network communication between MASs and can lead to MAS instability. To solve state time delay and state constraints, we construct a composite Lyapunov–Krasovskii (L–K) functional and propose an adaptive preset time control strategy. The composite L–K functional contains two parts: a barrier Lyapunov function to ensure that all states meet constraint requirements and an L–K functional to eliminate the influence of state time delay on MASs. External disturbances and the time derivatives of the L–K functionals are defined as unknown functions, estimated using a fuzzy logic system, thus simplifying complex calculations and improving the control scheme’s resistance to external disturbances. To effectively alleviate the influence of unknown control directions on MASs, we employ the traditional Nussbaum function. In practical MAS applications, control input constraint, which is caused by the limited driving ability of agents, often imposes constraints on control inputs. Mishandling these constraints can compromise system performance or lead to instability. Addressing control input constraints is a huge theoretical challenge and a practical requirement. This paper uses the mean value theorem to deal with the control input constraint problem effectively. Finally, the bounded stability of the closed-loop system is analyzed using the Lyapunov stability theory, ensuring that the output error satisfies constraints within the preset time. Numerical simulations and two-stage chemical reactor simulations illustrate the effectiveness and feasibility of the designed control scheme. In summary, the adaptive fuzzy preset time control strategy presented in the paper successfully achieves the consensus stability of nonlinear MASs.