Controller synthesis for reusable agents of consensus networks

We consider consensus problem over networks where each agent is modeled as a class of LTI systems. The objective is to make certain output of each agent converge to the (weighted) average of their initial conditions. To solve this consensus problem, we equip each plant with a local dynamic output-feedback controller. The system configuration allows us to decompose the networked system into subsystems characterized by the eigenvalues of Laplacian associated with the network topology. Having recognized that all the eigenvalues of Laplacian are bounded in a circle region, we cast each eigenvalue as an norm bounded uncertainty and use the robust control framework to evaluate the stability of each subsystem. We derive the sufficient condition to ensure that only the zero eigenvalue of Laplacian can touch the boundary of the circle. Based on that condition, we develop sufficient conditions to guarantee the marginal stability of the overall system, which allows us to use LMI approach to synthesize the controller and establish the convergence property of the system. Fianlly, we adopt a two-degree of freedom controller to improve the performance of the system as well as save the controller output energy.