Consensus of Linear Discrete-Time Multi-Agent Systems: A Low-Gain Distributed Impulsive Strategy

This paper aims to investigate the semiglobal consensus problem of a class of linear discrete-time multi-agent systems with distributed impulsive control. First, a novel distributed impulsive strategy is presented for achieving semiglobal consensus by considering low-gain feedback control, in which the magnitude of the impulsive protocol converges to zero when the low-gain parameter tends to zero. By utilizing the Lyapunov function and low-gain theory, a parametric discrete-time Riccati equation is considered for calculating impulsive control gain matrix. Furthermore, based on the low-and-high-gain approach, another distributed impulsive strategy is proposed. Moreover, two algorithms are then presented to derive the control gain matrices of distributed impulsive protocols for meeting different performance requirements. Subsequently, the applicability of proposed strategies is validated through two examples.