Cooperative control of multi-agent system based on two-delay feedback

The method of designing distributed H_∞ two-delay feedback controllers for arbitrary-order multi-agent system with undirected topology is studied in this paper. By introducing H_∞ two-delay controller into multi-agent system, the consensus performance of the system is improved. Firstly, by using the matrix theory, the multi-agent system satisfying the H_∞ performance index is decomposed into several independent subsystems satisfying corresponding H_∞ performance indexes with respect to the eigenvalues of the Laplacian matrix. Then, the problem of designing distributed H_∞ two-delay controllers for the resultant subsystems is converted into the stabilization problem of a set of quasi-polynomials, which can be solved by employing the D-decomposition method. Finally, the set of distributed H_∞ two-delay feedback control parameters is analytically obtained by finding the intersection of the control parameter regions for all the decomposed subsystems satisfying the corresponding H_∞ performance index. The simulation results demonstrate the effectiveness of the proposed method.