# zbMATH — the first resource for mathematics

Consensus and its $${\mathcal L}_2$$-gain performance of multi-agent systems with intermittent information transmissions. (English) Zbl 1256.93016
Summary: This article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network, where each agent can only communicate with its neighbors intermittently. A class of control algorithms is first introduced, using only intermittent relative local information. By combining tools from switching systems and Lyapunov stability theory, some sufficient conditions are established for consensus of multi-agent systems without any external disturbances under a fixed strongly connected topology. Theoretical analyses are further provided for consensus of multi-agent systems in the presence of external disturbances. It is shown that a finite $${\mathcal L}_2$$-gain performance index for the closed-loop multi-agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalized algebraic connectivity of the strongly connected topology. The results are then extended to consensus with prescribed $${\mathcal L}_2$$-gain performance with a virtual leader where the underlying topology is not necessarily strong connected or contain a directed spanning tree. Numerical simulations are finally provided to verify and visualize the theoretical analysis.

##### MSC:
 93A14 Decentralized systems 68T42 Agent technology and artificial intelligence
Full Text: