Average consensus seeking of high-order continuous-time multi-agent systems with multiple time-varying communication delays

Abstract

The average consensus problem of high-order multi-agent systems with multiple timevarying communication delays is investigated in this paper. By using the idea of state decomposition, the condition for guaranteeing average consensus is converted into verifying the stability of zero equilibrium of disagreement system. Considering multiple time-varying communication delays, LyapunovKrasovskii approach in time-domain is employed to analyze the stability of zero equilibrium. With the help of Free-weighting Matrices (FWM) approach, the tolerant upper bounds on communication delays can be obtained through solving feasible linear matrix inequalities (LMIs). Delay-dependent stability criteria for both strongly-connected fixed and switching topologies are provided in the main results. Further, the conclusion is extended to the case of jointly-connected switching topologies. Numerical examples and simulation results are given to demonstrate the effectiveness and the benefit on reducing conservativeness of the proposed method.

Decentralized H∞ consensus protocol for a class of high-order multiagent systems

“…Hence, as t → ∞ , all the agents achieve consensus on x a . Therefore, the regulated output defined in describes the MAS desired behavior to achieve consensus on a constant position x a , and this completes the proof.Remark It is worth mentioning that implies a consensus protocol similar to and . For instance, in , a consensus protocol was proposed for n th‐order MASs under undirected networks as follows: where denoted the protocol gains, which were designed based on all the nonzero eigenvalues of the network Laplacian matrix.…”

“…The average consensus problem in high‐order MASs under undirected networks was studied in . In , the consensus problem for high‐order MASs under undirected networks and in the presence of time‐varying communication delays was studied, and in , a consensus protocol for high‐order singular MASs under directed networks was proposed.…”

Consensus seeking of delayed high-order multi-agent systems with predictor-based algorithm

“…In synchronously-coupled algorithm, self-delays introduced for each agent in the coordination part equal the corresponding communication delays, while asynchronouslycoupled algorithm requires each agent to use its delayed state with the delay different from the corresponding communication delay, or use its current state to compare with its delayed neighboring agents' states. Consensus convergence of synchronously-coupled algorithm depends on the communication delay strictly for the multi-agent systems under fixed [19,29,33,37] or switched topologies [4,6,17,24,30,32,38]. With proper control parameters, differently, the stationary consensus algorithms in asynchronously-coupled form is convergent without any relationship to the communication delay value for the first-order, second-order and high-order agents [10,11,12,21,27].…”

Average consensus in multi-agent systems with uncertain topologies and multiple time-varying delays

“…One goal of this paper is to lift this constraint by considering balanced digraphs (directed graphs). Note that average consensus problem and leader-following consensus problem of high-order multi-agent systems with multiple time-varying delay are also treated in [37] and [39], respectively.…”

“…The above mentioned works [34,[36][37][38][39] implicitly assume the interaction strengths or link weights can be exactly measured. In other words, external disturbances and communication uncertainties have been ignored.…”