Event-Triggered <i>H_∞ </i> Consensus of Leader-Follower Multi-Agent Systems Under ADT Switching Topologies

This paper is concerned with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> control problem of leader-follower multi-agent systems under switching topology. The switching between the topologies is assumed to satisfy an average dwell time constraint. Considering the time delay introduced by sampling, a time-delay error system is established. To conserve bandwidth resources, an event-triggered approach is employed. By constructing a Lyapunov-Krasovskii functional, a sufficient condition for the exponential stability of the switching time-delay error system under average dwell time is provided in the form of Linear matrix inequalities. Then, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> controller is designed to guarantee both exponential stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> performance of the time-delay error system. Furthermore, the effects of sampling time and the threshold of the event-triggered mechanism on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> performance are discussed. Finally, a numerical example demonstrates the effectiveness of the proposed approach.