The integration of event-triggered and self-triggered control mechanisms has gained attention as a resource-efficient alternative to periodic control in multi-agent systems (MAS). This study proposes a framework analysis that unifies disturbance rejection, task planning, and H∞ consensus control under both event- and self-triggered paradigms. The work highlights theoretical formulations, comparative stability guarantees, and computational trade-offs in distributed settings. The study establishes disturbance attenuation bounds using H∞ norms, derive triggering conditions to prevent Zeno behaviour, and illustrate framework-level implications for large-scale task planning. This paper develops a comparative framework, highlighting the stability conditions, triggering mechanisms, and performance guarantees under H∞ consensus constraints. The proposed framework demonstrates applicability in cooperative robotics, distributed manufacturing systems, and resilient networked control applications.