Consensus of discrete‐time heterogeneous multi‐agent systems in noisy environments without velocity transmission

Abstract This paper investigates consensus control of discrete‐time heterogeneous multi‐agent systems with multiplicative noise. As the frequent absence of velocity sensors in real industrial environments, a control protocol is developed using absolute velocity and relative position measurement information. Then, the consensus control issue is reformulated as the stability issue of stochastic difference equations. By choosing an appropriate Lyapunov function, the above stability issue is studied, and the sufficient conditions for leader‐free and leader‐following discrete‐time heterogeneous multi‐agent systems to achieve both mean‐square and almost‐sure consensus are derived, respectively. Finally, numerical simulations are provided to validate the effectiveness of the main results.