Bacteria, bees, and birds often work together in groups to find food. A group of mobile wheeled robots can be designed to coordinate their activities to achieve a goal. Networked cooperative uninhabited air vehicles (UAVs) are being developed for commercial and military applications. In order foe such multiagent systems to succeed it is often critical that they can both maintain cohesive behaviors and appropriately respond to environmental stimuli. In this paper, we characterize cohesiveness of discrete-time multiagent systems as a boundedness or stability property of the agents' position trajectories and use a Lyapunov approach to develop conditions under which local agent actions will lead to cohesive group behaviors even in the presence of i) an interagent "sensing topology" that constrains information flow, where by "information flow," we mean the sensing of positions and velocities of agents, ii) a random but bounded delay and "noise" in sensing other agents' positions and velocities, and iii) noise in sensing a resource profile that represents an environmental stimulus and quantifies the goal of the multiagent system. Simulations are used to illustrate the ideas for multivehicle systems and to make connections to synchronization of coupled oscillators.