Control Architecture for Synchronization and Tracking in Descriptor Multi-Agent Systems

A control architecture is proposed for a descriptor multi-agent system to achieve the following objectives in the closed loop: i) the state response is impulse-free, and ii) the states of follower agents synchronize with the states of leader agent satisfying a pre-specified minimum decay rate (helps to regulate the synchronization speed). By performing a sequence of system transformations through orthogonal matrices, and using a parametric robust control framework, the synchronization problem is addressed, where the associated gain parameters are computed by solving a linear matrix constraint problem, and using the largest eigenvalue of network Laplacian matrix. The implementation of some feedforward gain matrices ensures that the constant reference tracking objective is also achieved, in addition to the synchronization. The proposed algorithm is demonstrated with a numerical example.