Robust Distributed Adaptive Consensus for Discrete-Time Multiagent Systems with Uncertain Topologies

Abstract This paper considers the stochastic consensus problem of high-order linear discrete-time multiagent systems (MASs) with uncertain topologies and external disturbances. The randomly switching interaction signed topologies are governed by a time-homogenous Markov chain with incomplete knowledge of the transition probabilities. Based on Lyapunov function theory and adaptive control strategies, we employ a homogeneous parameter-dependent Lyapunov function to propose sufficient conditions under a set of linear matrix inequality (LMI) constraints. A free-weighting matrix method is introduced to give the proposed LMIs extra freedom to search feasible solutions. Furthermore, the adaptive controllers applied in this paper are independent of topologies and fully distributed; i.e., the system achieves robust consensus without continuously updating the controller and dealing with global data. Additionally, we extend the theoretical framework to analyze the disturbance rejection performance of MASs under the stochastic process. Two numerical examples are provided to show the effectiveness of the algorithms.