Consensus control of second-order stochastic discrete-time multi-agent systems without velocity transmission

This article studies the almost-sure and the mean-square consensus control problems of second-order stochastic discrete-time multi-agent systems with multiplicative noises. First, a control law based on the absolute velocity and relative position information is designed. Second, considering the existence of multiplicative noises and nonlinear terms with Lipschitz constants, the consensus control problem is solved through the use of a degenerated Lyapunov function. Then, for the linear second-order multi-agent systems, some explicit consensus conditions are provided. Finally, two sets of numerical simulations are performed.