On the estimation of the domain of consensus for discrete-time multi-agent systems subject to actuator saturation

摘要

For a discrete-time linear system that has an open-loop pole outside the unit circle and is subject to actuator saturation, global asymptotic stabilization cannot be achieved. As a consequence, a discrete-time multi-agent system containing such an actuator saturating agent can only reach regional consensus, that is, the consensus can be achieved only if the initial state of each agent resides in a region of the state space. The region of all these initial states is referred to as the domain of consensus. In general, the exact characterization of the domain of consensus is impossible. In this paper, we consider the problem of estimating the domain of consensus of a discrete-time multi-agent system with an agent subject to actuator saturation. We establish a set of conditions under which an ellipsoidal set can be used as an estimate of the domain of consensus. Based on these conditions, an LMI-based optimization problem is formulated for obtaining the largest ellipsoidal estimate of the domain of consensus. Simulation results illustrate the effectiveness of the proposed approach and show the relationship between the size of the largest ellipsoidal estimate and the communication topology of the multi-agent system.