H∞ Control for Multi-Agent Systems under Two-Way Amplify-and-Forward Relay Networks: The Event-Trigger Case

This paper addresses the finite-horizon H∞ control problem for the two-way amplify-and-forward (AF) relay-assisted multi-agent system. To enhance communication quality and mitigate channel fading effects, a two-way AF relay protocol is introduced to coordinate data transmission among agents. Based on channel statistical characteristics and incorporating an event-triggered mechanism, this paper designs an H∞ control protocol to ensure that the dynamic system satisfies the specified H∞ performance metrics within a finite horizon. First, sufficient conditions are established for the system to satisfy the given H∞ performance requirements. Then, by solving two coupled backward Riccati difference equations under the H∞ performance constraints, the feedback gain matrix of the event-triggered controller is determined. Finally, the effectiveness of the proposed control strategy is verified through numerical simulations.