$$L_2$$ Leader-Following Consensus of Second-Order Nonlinear Multi-agent Systems with Disturbances Under Directed Topology via Event-Triggered Control Scheme

Abstract

This paper addresses the \(L_2\) leader-following consensus problem for second-order multi-agent systems with nonlinear dynamics and external disturbances under directed topology. The event-triggered control (ETC) scheme with a new ETC protocol and an event-triggered condition has been introduced. In the control protocol, two parameters which are constrained by the predefined performance index are designed to adjust the convergence rate of the system. Based on the directed graph theory, we construct a Lyapunov function, and then prove theoretically that the system can achieve leader-following consensus without disturbance, and a predefined \(L_2\) gain performance index can be guaranteed under the zero initial condition when disturbances exist. A simulation example is provided to verify the theoretical results.