Mean-Square Quasi-Consensus for Discrete-Time Multi-Agent Systems with Multiple Uncertainties

This study investigates mean-square quasi-consensus for a class of linear discrete-time multi-agent systems with external disturbances, where both the system model and network uncertainties are considered. By introducing adjustable parameters, a more generalized modeling of the internal system uncertainties is achieved, and the network uncertainties among agents are described by Bernoulli variables. This study employs a method combining the parametric algebraic Riccati equation (PARE) and linear matrix inequalities, and a novel auxiliary lemma is developed based on the properties of the PARE. The results demonstrate that, under the designed control protocol, by satisfying the conditions related to the expectations of random uncertainties and network uncertainties, the multi-agent system can achieve mean-square quasi-consensus. Finally, numerical simulation examples are conducted to demonstrate the effectiveness of the results obtained in this study, and the fluctuation in the error trajectory curve is smaller than some existing results.