Time-Constrained Consensus With Reduced Agent Interactions for Matrix-Scaled Networks

This letter proposes a distributed control method for matrix-scaled multi-agent networks aimed at achieving practical convergence within a user-defined time frame. The control law of each individual agent relies only on information from neighboring agents and is updated at discrete intervals determined by state-dependent triggering functions, reducing the frequency of agent interactions. To this end, first, the controller is augmented with a time-varying gain. Then, the dynamics of the closed-loop system over the finite-time interval is transformed into an infinite-time frame using time scaling. Lyapunov-based analysis is employed to derive suitable triggering conditions that guarantee the asymptotic convergence of the time-transformed system, thereby ensuring the prescribed-time convergence of the original system. Furthermore, a practical prescribed-time event-triggered control scheme is proposed that excludes Zeno behavior. Simulation results validate the effectiveness of the proposed controller, even in the presence of external disturbances.