Reliable Leader-Following Consensus of Discrete-Time Semi-Markovian Jump Multi-Agent Systems

This paper is concerned with the leader-following reliable consensus control problem of a class of discrete-time semi-Markovian jump multi-agent systems. Two stochastic jump processes are employed to characterize the changes of system parameters and actuator faults. The abrupt changes of the agent parameters are described by a discrete semi-Markovian process. Another discrete Markovian jump process represents the actuator faults which stochastically occur and change during the operation of the subsystem. Firstly, sufficient conditions for guaranteeing the leader-following consensus are derived. Secondly, a non-fragile distributed reliable consensus control protocol is presented for the underlying system with additive norm bounded gain perturbations. Thirdly, the proposed approach of distributed consensus controller is extended to the scenario which system parameters are uncertain and fault transition probability matrix is confined to a polytope composed of multiple vertices. Finally, two examples are provided to illustrate the efficacy of the presented results.