This technical note focuses on finite-time rendezvous problems which refer to agreement on states in finite time within certain available information range. Using semistability theory for discontinuous dynamical systems, we develop a framework for designing finite-time semistable rendezvous protocols for multiagent dynamical systems. Specifically, we present distributed nonsmooth static state and dynamic output feedback controller architectures for finite-time rendezvous with a novel two-step proof of stability and finite-time convergence.