Finite-Horizon H∞ Bipartite Consensus Control of Cooperation–Competition Multiagent Systems With Round-Robin Protocols

This article focuses on the finite-horizon
$\mathcal {H}_{\infty }$
bipartite consensus control problem for a class of discrete time-varying cooperation–competition multiagent systems (DTV-CCMASs) with the round-robin (RR) protocol. The cooperation–competition relationship among agents is characterized by a signed graph, whose edges are with positive or negative connection weights. Specifically, a positive weight corresponds to an allied relationship between two agents and a negative one means an adversary relationship. The data exchange between each agent and its neighbors is orchestrated by an RR protocol, where only one neighboring agent is authorized to transmit the data packet at each time instant, and therefore, the data collision is prevented. This article aims to design a bipartite consensus controller for DTV-CCMASs with the RR protocol such that the predetermined
$\mathcal {H}_{\infty }$
bipartite consensus is satisfied over a given finite horizon. A sufficient condition is first established to guarantee the desired
$\mathcal {H}_{\infty }$
bipartite consensus by resorting to the completing square method. With the help of an auxiliary cost combined with the Moore–Penrose pseudoinverse method, a design scheme of the bipartite consensus controller is obtained by solving two coupled backward recursive Riccati difference equations (BRRDEs). Finally, a simulation example is given to verify the effectiveness of the proposed scheme of the bipartite consensus controller.