Finite-Time Prescribed Performance <i>H</i> _∞ Control of Multi-Agent Systems Based on Sample-Data Event-Triggered Mechanism

This study considers the finite-time prescribed performance <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking consensus control problem in nonlinear multi-agent systems with time-varying disturbance and designs a distributed event-triggered control strategy. First, a class of time-dependent error performance constraint functions is introduced to effectively address the negative impact of disturbances on the transient and steady-state performance of a system. Second, a dynamic event-triggered protocol defined using periodic sampling data is proposed to reduce the information transmission between agents and decrease the controller’s update frequency. Third, the designed dynamic event-triggered mechanism is combined with the finite-time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control theory, and sufficient conditions for the system to achieve tracking consensus in a finite time are obtained by employing the Lyapunov stability theory and linear matrix inequality. Finally, the feasibility of the proposed distributed control strategy is verified through numerical simulations and practical examples.