Cooperative Control of Multi-agent System Based on Two-Delay Feedback

The method of designing distributed H-infinity two-delay feedback controllers for arbitrary-order multi-agent system with undirected topology is studied in this paper. By introducing H-infinity 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-infinity performance index is decomposed into several independent subsystems satisfying corresponding H-infinity performance indexes with respect to the eigenvalues of the Laplacian matrix. Then, the problem of designing distributed H-infinity 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-infinity 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-infinity performance index. The simulation results demonstrate the effectiveness of the proposed method.