Impulsive Consensus Protocols of Discrete-Time Second-Order Multiagent Systems With Lipschitz Nonlinear Dynamics

This article investigates the leaderless consensus problem of discrete-time second-order nonlinear multiagent systems with the switching topology via the impulsive control. By defining a weighted average state associated the topology structure, two types of impulsive protocols are proposed: 1) dynamical consensus and 2) static consensus. The form drives all the agents toward the weighted average state, while the latter ensures that each agent tends to an agreed position. Unlike the existing impulsive protocols exerting impulsive actions on all the state variables of the agents, the proposed impulsive protocols only regulate the agents’ velocity vectors in an impulsive fashion throughout the consensus process. The introducing of the timer-dependent weighted double Lyapunov functions plays a key role in consensus analysis, which is able to exploit the relationship among the discrete-time agent’s dynamics, the impulsive protocols, and the communication topology. Sufficient conditions are derived to design the gain matrices of the impulsive protocols, which are dependent on the current impulse interval. The numerical results show that the variable gain-based design approach can tolerate larger variation in impulse intervals for impulsive consensus.