Sample-and-hold solution of a consensus problem with nonlinear dynamics and input/output disturbances

The consensus problem of multi-agent systems (MASs) over directed graphs is analyzed in this paper. A sampled-data control law is induced from a nonlinear consensus protocol (continuous or not) by implementing feedback stabilization methods, in the sample-and-hold sense. Under the edge agreement framework, we show that consensus in a strongly connected network can be achieved over some suitable finite time. Furthermore, if an arbitrarily large and bounded actuator disturbance affects the MAS, we show that the sampled-data controller can be robustified to still guarantee the agreement. The case with observation errors is investigated too. The agent drift dynamics are required to be globally Lipschitz and bounded. Numerical simulations are finally proposed to validate the results.