H∞ leader-following consensus of multi-agent systemswith channel fading under switching topologies: a semi-Markov kernel approach

This paper focuses on the leader-following consensus problem of discrete-time multi-agent systems subject to chan-nel fading under switching topologies. First, a topology switching-based channel fading model is established to de-scribe the information fading of the communication channel among agents, which also considers the channel fadingfrom leader to follower and from follower to follower. It is more general than models in the existing literature thatonly consider follower-to-follower fading. For discrete multi-agent systems, the existing literature usually adoptstime series or Markov process to characterize topology switching while ignoring the more general semi-Markov pro-cess. Based on the advantages and properties of semi-Markov processes, discrete semi-Markov jump processes areadopted to model network topology switching. Then, the semi-Markov kernel approach for handling discrete semi-Markovjumpingsystemsisexploitedandsomenovelsufficientconditionstoensuretheleader-followingmeansquareconsensusofclosed-loopsystemsarederived. Furthermore, the distributed consensus protocolis proposed by means of the stochastic Lyapunov stability theory so that the underlying systems can achieveH infinity consensus performance index. In addition, the proposed method is extended to the scenario where the semi-Markov kernel of semi-Markovswitching topologies is not completely accessible. Finally, a simulation example is given to verify the results proposedin this paper. Compared with the existing literature, the method in this paper is more effective and general.