Leader-following second-order consensus in multi-agent systems with sampled data via pinning control

This paper studies the second-order consensus in multi-agent systems with sampled position and velocity data via pinning control. The distributed pinning consensus protocols with second-order dynamics are designed, where both sampled position and velocity data are employed. Necessary and sufficient conditions are derived for reaching second-order consensus by combining the algebraic graph theory and the analytical method. According to the obtained consensus criteria, the second-order leader-following consensus can be reached if and only if the sampling period, the coupling gain, and the pinning gains satisfy some derived algebraic inequalities. Moreover, it is found that second-order consensus in multi-agent systems cannot be reached with only sampled position data in the pinning controllers. Finally, the effectiveness and correctness of our theoretical findings are demonstrated by some numerical examples.