Leader-Following Consensus Considering Effects of Agents on Each Other via Impulsive Control: A Topology Dependent Average Dwell Time Approach

Abstract

This paper intends to investigate the consensus problem of a nonlinear multi-agent system with new nonlinear terms added to the dynamics of each agent in the leader-following framework with impulsive control. The main contribution of this paper is introducing these new terms expressing the effect of each agent on neighbor agents. The new terms called effect terms (ETs) are considered with time-varyingdelay. Moreover, the communication interactions among all agents are addressed by a set of consensusable and unconsensusable switching topologies. In particular, the topology-dependent average dwell time (TDADT), as one of the significant practical analysis methods for switched systems, has been calculated for each topology. The globally uniformly exponentially stability (GUES) for the consensus error dynamics is analyzed by employing algebraic graph theory and a multiple discontinuous Lyapunov function approach (MDLF) regarding separate Lyapunov functions for impulse instants. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that consensus can be achieved. Finally, the effectiveness of the theoretical analysis is corroborated by a numerical example.