On global and local consensusability of multi-agent systems with input constraint and uncertain initial conditions

In this paper we consider the consensuability problem of linear multi agent systems in the presence of input constraint and uncertain state initial conditions. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, we present low computationally on demanding LMI conditions to explicitly design a distribute protocol to guarantee network consensuability. Input norm bound constraint is full-filled despite of the uncertain network initial conditions. This is of practical interest in a real applications of consensus protocol because the input bound (i.e. due to actuator saturation) may not be easily fulfilled as the control at each node depends on the state and its uncertain initial value of the neighboring agents. The results hold for both undirected and directed graph. A numerical example about the leader-follower scenario is shown to validate the theoretical findings. From the computational point of view, the LMI conditions have the merit to be easily solved by the MATLAB toolbox as their number and size do not depend on network size. This enables their use to control large scale multi agent systems.