Distributed PFI Consensus Control for Discrete-Time Second-Order Stochastic Multi-Agent Systems*

The distributed proportional-fragment-integral (PFI) consensus control problem for discrete-time second-order stochastic multi-agent systems(MASs) is investigated in this paper, which is an extension of general proportional-integral control. Firstly, mean square(m.s.) and almost sure(a.s.) exponential stability criterion is established for discrete-time stochastic linear difference equation with fragment-integral term. Then, based on this stability criterion, sufficient conditions for achieving m.s. and a.s. consensus of discrete-time stochastic MASs under distributed discrete PFI control protocol are obtained, indicating that the discrete fragment-integral term can facilitate stochastic MASs consensus. Finally, a simulation example is given to verify the validity of the theoretical results.