Dynamic gain scheduling control design for linear multiagent systems subject to input saturation

This paper considers the finite-time bipartite consensus problem governed by linear multiagent systems subject to input saturation under directed interaction topology. Due to the existence of input saturation, the dynamic performance of linear multiagent systems degrades significantly. For the improvement of the dynamic performance of systems, a dynamic gain scheduling control approach is proposed to design a dynamic Laplacian-like feedback controller, which can be obtained from the analytical solution of a parametric Lyapunov equation. Suppose that each agent is asymptotically null controllable with bounded control, and that the corresponding interaction topology of the signed directed graph with a spanning tree is structurally balanced. Then the dynamic Laplacian-like feedback control can ensure that linear multiagent systems will achieve the finite time bipartite consensus. The dynamic gain scheduling control can better improve the bipartite consensus performance of the linear multiagent systems than the static gain scheduling control. Finally, two examples are provided to show the effectiveness of the proposed control design method.