Event-triggered leader-following consensus of nonlinear semi-Markovian multi-agent systems via improved integral inequalities

This paper studies the leader-following event-triggered consensus of multi-agent systems with nonlinear dynamics and semi-Markov jump. The information on transition rates is incompletely known. First, by applying weighted orthogonal polynomials, two new integral inequalities are established, which include some existing ones. Second, an event-triggered scheme is presented to save the precious communication resources. After constructing an augmented Lyapunov–Krasovskii functional, a few sufficient conditions are derived to achieve the leader-following event-triggered consensus by utilizing the presented inequalities to manipulate the derivative of the functional. Finally, numerical simulation shows the effectiveness of the proposed method.