H∞ group consensus for partial-state coupled linear systems with fixed and switching topologies in the cooperation-competition networks

Abstract

The H∞ group consensus problem is investigated for partial-state coupled linear systems with fixed and switching topologies in the cooperation-competition networks. The weights are positive in the cooperative sub-networks, and the weights are negative in the competitive sub-networks. For the case with fixed topology, a class of consensus protocol is constructed by using the coupling partial-state information among the nodes, it is proved that H∞ group consensus can be achieved if the coupling strength within each sub-network is larger than a given positive value and the feedback gain matrix is appropriately designed. It should be emphasized that the in-degree condition between different sub-networks is removed and the sub-network topology is not required to be connected, the results show the competition relationship plays a positive role for H∞ group consensus. The above results can also be extended to the case with switching topologies, the adaptive protocol is designed for H∞ group consensus, where the coupling strengths within each sub-network can be dynamically adjusted with the evolution of the system. Finally, two simulation examples are presented to verify the obtained theoretical results.