L 2 — L ∞ control for leader-following coordination of second-order multi-agent systems

This paper deals with L 2 — L ∞ control for leader-following coordination of second-order multi-agent systems with external disturbance and time-delay on fixed topology. In practical applications, the peak value of the controlled output is often required to be within a certain range and the ranges of the position and the velocity are different, so we introduce the weighted coefficients for the controlled outputs of the position and the velocity separately. Then, we obtain a multi-agent system of the model.Based on the Lyapunov-Krasovskii theory, both networks with and without time-delay are analyzed for leader-following corrdination of the position vector and the velocity vector with the desired L 2 — L ∞ performance. Furthermore, sufficient conditions in terms of bilinear matrix inequality are given to guarantee the consensus problems for the multi-agent systems with and without time-delay sparately. Finally,numerical simulations are provided to show the effectiveness of our strategies.