Robust Consensus for Continuous-Time Multiagent Dynamics

Abstract

This paper investigates consensus problems for continuous-time multiagent systems with time-varying communication graphs subject to input noise. Based on input-to-state stability and integral input-to-state stability, robust consensus and integral robust consensus are defined with respect to $L_\infty$ and $L_1$ norms of the noise function, respectively. Sufficient and/or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions. The results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance. The $\epsilon$-convergence time is obtained for the consensus computation on directed and $K$-bidirectional graphs.