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The problem of event-triggered guaranteed cost consensus for nonlinear multi-agent systems with time delay and uncertain parameters is solved in this paper. First, a distributed event-triggered strategy is presented, by which control protocol is updated only at the triggering time instants, leading to significant saving of communication resources. Second, based on the Lyapunov method and the proposed event-triggered strategy, some criteria are obtained to ensure that guaranteed cost consensus can be achieved. Moreover, it is proved that the Zeno behavior is excluded under the proposed event-triggered scheme. Third, an algorithm is given to design suitable control gains in terms of linear matrix inequalities. Finally, the validity of the proposed results in this paper is verified via numerical simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the leader-following bipartite consensus problem for second-order multi-agent systems with nonlinear dynamics, node-delay and signed digraph topology. By using pinning control strategies, an event-triggered controller is designed to achieve bipartite consensus in multi-agent systems, where a novel event-triggered function is proposed. Two cases are discussed in this paper according to whether the node-delay is differentiable or not. When the node-delay is differentiable, an LMI (Linear Matrix Inequality) condition is derived for reaching bipartite consensus in multi-agent systems by using M -matrix theory. When the node-delay is non-differentiable, some bipartite consensus conditions are developed based on Jensen inequality and the reciprocally convex approach. Moreover, it is shown that Zeno-behavior can be avoided for the designed event-triggered controller. Finally, some numerical examples are provided to illustrate the effectiveness and correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the problem of finite-time consensus of linear multi-agent systems with input time-varying delay by employing a non-fragile control scheme, where the network topology of the communication process among agents is subject to a switching directed graph. The main intention of this paper is to propose a non-fragile controller design protocol that guarantees the finite-time stability of the resulting closed-loop system even in the presence of time-varying delay in the input channel. Sufficient conditions for the solvability of such a problem are obtained by using the Lyapunov–Krasovskii stability theory, the algebraic graph theory and some integral inequalities. Based on the obtained conditions, an explicit expression of the desired non-fragile control gain matrix is then presented. Finally, an illustrative example is given to exhibit the applicability and effectiveness of the proposed finite-time consensus control design method. [ABSTRACT FROM AUTHOR]

Highlights This paper studies the consensus problems for the two types of double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays: the DIFOMAS with symmetric time delays over undirected topology, and the DIFOMAS with asymmetric time delays over directed topology. The main contributions of this paper are as follows: • Consider the double-integrator fractional-order dynamics. • Consider the nonuniform time-delays, which contain up to n(n-1) different values when the DIFOMAS consists of n agents. • Consider the dynamics of each agent containing two state-variable with different fractional orders. • Obtain the two kinds of the upper bound of time-delays about Theorems 1 and 2 and the corollaries of Theorems 1 and 2. Abstract This paper addresses the distributed consensus control for a double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays. A general model of the DIFOMAS is introduced by such case: the dynamic model of each agent contains two state variables with different fractional orders. The consensus conditions on the two kinds of network topology and the nonuniform time-delays can be obtained by using the generic model: the DIFOMAS with symmetric time-delays over undirected topology, and the DIFOMAS with asymmetric time-delays over directed topology. With the help of matrix theory, Laplace transform and graph theory, two kinds of upper bounds of time-delays are derived to ensure the DIFOMAS with nonuniform time-delays can reach consensus. Finally, some numerical simulations with different parameters are offered to illustrate the feasibility and effectivity of the results derived. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive distributed event-triggered fault-tolerant consensus problem for a class of multi-agent systems with time delays and external disturbance. The communication faults between the agent and its neighbours are considered, and a fault-tolerant control mechanism is designed to overcome the communication faults. Moreover, a distributed event-triggered mechanism is constructed based on the distributed errors, and hence the communication burden can be reduced. Combining the Lyapunov stability theorem with the Lyapunov-Krasovskii function, it verifies that the consensus tracking errors are bounded with the guaranteed security performance, and the time delays phenomenon can also be compensated. Finally, the effectiveness and utility of the proposed control method are fully validated by two simulation examples. [ABSTRACT FROM AUTHOR]

The issue of stability and group output consensus is investigated for the discrete-time heterogeneous networked multi-agent systems with communication constraints(e.g., time delays and data loss) in this paper. Firstly, the couple-group output consensus is analyzed theoretically, the communication constraints are compensated by the prediction method. Secondly, the necessary and sufficient condition is given to ensure the stability of the system, achieve the couple-group consensus with reference input control, and relax the topology constraint of in-degrees balance by cooperative-competitive interactions. Furthermore, the result of couple-group consensus is extended to multi-group consensus based on a novel predictive control algorithm. Finally, a numerical simulation shows that the proposed networked predictive control method can effectively overcome the communication constraints, the dynamic performance and control effect are similar to the traditional control without communication constraints. [ABSTRACT FROM AUTHOR]

In this paper, we study the cooperative output regulation problem for discrete-time linear time-delay multi-agent systems subject to jointly connected switching networks. Our distributed control law is composed of a purely decentralized control law and a distributed switched observer. In contrast to the same problem with static networks, the closed-loop system of this paper is a switched system, the stability analysis of the closed-loop system cannot be conducted by the existing frequency domain technique. Therefore, we need to establish two lemmas to lay the foundation for solving the problem and then present the solution to the problem by a distributed dynamic output feedback control law. An example is used to illustrate our approach. [ABSTRACT FROM AUTHOR]

This paper focuses on the consensus control and fault estimation problems for a class of time-delayed multi-agent systems with Markov switching topologies. Two different event-triggered mechanisms are adopted with hope to reduce burden of shared network and improve energy efficiency. Under Markov process, by establishing the consensus control protocol and designing a novel adaptive fault estimation observer, the consensus control and fault estimation problems are transformed into two stochastic stability problems in different forms. Then, according to the switching Lyapunov function method and free-weighting matrix technique, two delay-dependent stability criteria on the consensus control and fault estimation are derived, respectively. However, the two criteria containing nonlinear coupling terms are not standard linear matrix inequalities (LMIs) and cannot be solved directly with the LMI toolbox. In order to eliminate the coupling terms, two improved path-following algorithms are presented. These algorithms depend on the initial conditions, so it is very crucial to choose the appropriate preset parameters. The computational complexity is increasing with the number of iterations, system size and matrix dimension, which is a fully new challenge for the study of consensus control and fault estimation of multi-agent systems. Based on the algorithms, the switching consensus controller gains and model gain matrices of fault estimation can be efficiently solved out. Finally, a simulation example of tailless fighter airplanes is given to illustrate the practicality and validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the consensus control and fault estimation problems for a class of time-delayed multi-agent systems with Markov switching topologies. Two different event-triggered mechanisms are adopted with hope to reduce burden of shared network and improve energy efficiency. Under Markov process, by establishing the consensus control protocol and designing a novel adaptive fault estimation observer, the consensus control and fault estimation problems are transformed into two stochastic stability problems in different forms. Then, according to the switching Lyapunov function method and free-weighting matrix technique, two delay-dependent stability criteria on the consensus control and fault estimation are derived, respectively. However, the two criteria containing nonlinear coupling terms are not standard linear matrix inequalities (LMIs) and cannot be solved directly with the LMI toolbox. In order to eliminate the coupling terms, two improved path-following algorithms are presented. These algorithms depend on the initial conditions, so it is very crucial to choose the appropriate preset parameters. The computational complexity is increasing with the number of iterations, system size and matrix dimension, which is a fully new challenge for the study of consensus control and fault estimation of multi-agent systems. Based on the algorithms, the switching consensus controller gains and model gain matrices of fault estimation can be efficiently solved out. Finally, a simulation example of tailless fighter airplanes is given to illustrate the practicality and validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the distributed event-triggered control (ETC) problems for nonlinear stochastic multi-agent systems (MASs) with external disturbance and time-delay are discussed. The leader-following input-to-state actual exponential mean-square consensus (EMSC) criteria are established in networks containing a directed spanning tree. By devising appropriate Lyapunov–Krasovskii function, sufficient conditions for the model to achieve leader-following input-to-state actual EMSC are obtained. The control gain matrix is designed to realize the controller. The lower bounds of interexecution times are given to show that the Zeno-behavior will not appear. Besides, the validity of theoretical analyses is verified by simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive event-triggered consensus control problem for a class of linear multi-agent systems subject to cyber attacks and communication delays. To effectively alleviate unnecessary signals transmission among the agents and achieve the reasonable allocation of resources, an adaptive event-triggering scheme, whose threshold parameters are adaptively adjusted based on system performance needs, is proposed. The event-triggering scheme can achieve the discontinuous communication and significantly reduce the number of signals transmission while ensuring the desired control performance. By considering the communication scheme and consensus control protocol in a unified framework, the linear multi-agent system is reformulated as a time-delay error system. Sufficient conditions are developed to guarantee the asymptotical stability and security of time-delay error system. Moreover, a co-design for the gain of the controller and the parameters of the adaptive event-triggering scheme is provided. Finally, an example on the tunnel diode circuit system is given to show the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with distributed event-triggered consensus of a generally linear multi-agent system subjected to periodic denial-of-service (DoS) jamming attacks. First, a novel switched time-varying delay system model is established to describe consensus error dynamics. By virtue of the switched system and time delay system approaches, one constraint is obtained as a tradeoff between exponential convergence rate of consensus error and uniform lower bound of sleep intervals of periodic DoS jamming attacks. Second, sufficient conditions are derived to guarantee exponential consensus of the multi-agent system. Third, a co-design method is presented to determine the parameters of both the distributed event-triggered mechanism and consensus protocol. Furthermore, an algorithm is given to find the allowable uniform lower bound of sleep intervals and suboptimal distributed event-triggering parameters. Finally, an illustrative example is provided to verify the effectiveness of the proposed resilient event-triggering consensus design method against periodic DoS jamming attacks. [ABSTRACT FROM AUTHOR]

The problem of group consensus is considered for a class of discrete-time heterogeneous multi-agent systems(HMASs) with time delays in this paper. Due to network-induced time delays, the predictive scheme is proposed to compensate delays actively by using the received agents' outdate information, and a novel distributed protocol with prediction of states is designed. By getting rid of a conservation condition of in-degree balance which widely exists in relevant results, necessary and/or sufficient conditions are established for group consensus control of discrete-time HMASs. Finally, simulations are demonstrated that, under the proposed theoretical results, the performance of discrete-time HMASs with time delays is similar to that without delays. [ABSTRACT FROM AUTHOR]

The containment control problem using only sampled position data for second-order multi-agent systems (MAS) is studied in this paper. We first consider the delay-free case of the containment control protocol and obtain a necessary and sufficient condition regarding the network structure and the system parameters. Then, we obtain a similar necessary and sufficient condition for the case with time delay of the containment control protocol. Finally, several numerical simulations are performed to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper concerns about the iterative learning consensus control scheme for a class of multi-agent systems (MAS) with delay distributed parameter models. First, based on the framework of network topologies and using the nearest neighbor knowledge, a second-order iterative learning consensus control protocol is proposed. Next, under the proposed controller, a discrete dynamic system with respect to the iteration number variable is established and the consensus control problem is then converted to a stability problem of a discrete dynamic system. Furthermore, a sufficient condition for the convergence of the consensus errors between any two agents is obtained. Finally, the simulation examples illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the distributed input-constrained consensus problem for continuous-time high-order multi-agent systems with time-delays. Each agent's control input is constrained to lie in a nonconvex set. A distributed control algorithm is proposed to achieve consensus of the agents. Finally, we illustrate the theoretical result by a numerical example. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a self-triggered algorithm for leader-following consensus of general linear multi-agent systems with input time delay is proposed. It is shown that the leader-following consensus can be reached asymptotically and the Zeno-behaviour of triggering time sequences can be excluded. Under this algorithm, the next exact triggering time instant of each agent can be computed by the local information at the previous triggering time instant. Continuous communication, monitoring of measurement error and updating of controller input are thus avoided. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the adaptive event-triggered formation tracking control of a class of second-order multi-agent systems (MASs) with time-varying delay. Firstly, a distributed control protocol is constructed and some extended adaptive event-triggered schemes are presented, where the triggering thresholds rely on the real-time variation of the MASs but not not pre-selected constants. Then by choosing an augmented Lyapunov–Krasovskii functional (LKF), two delay-dependent criteria are formulated in terms of linear matrix inequalities (LMIs). Especially, during estimating the upper bound on LKF’s derivative, since some novel integral inequalities and a new convex technique are utilized, the conservatism can be greatly reduced. Finally, two numerical examples with some simulations are provided to illustrate our methods. [ABSTRACT FROM AUTHOR]

This paper examines the robust consensus problem of nonlinear multi-agent systems via a resilient controller subject to switching topology, wherein the effect of uncertainty in the form of additive perturbations and a randomly varying communication delay is considered in the control design. In particular, a directed graph is used to describe the interaction topology of the addressed multi-agent system and a stochastic variable obeying the Bernoulli distributed white sequences is incorporated to represent the randomness of delay. By utilizing the Lyapunov’s direct method and some matrix operations, a sufficient condition for mean-square asymptotic consensus of the addressed system is derived. Subsequently, the explicit characterization of the resilient control gain is obtained by means of linear matrix inequalities that can be effectively solved by using the ideas of convex optimization. An academic example is eventually presented to illustrate the significance and potency of the proposed control design strategy. [ABSTRACT FROM AUTHOR]

This paper addresses containment control of multi-agent systems with multiple interactive leaders. The containment control objective is two-fold: the leaders converge to a desired formation, and the followers move into the convex hull spanned by the leaders’ final positions. Some sampled-data based protocols are proposed, which are effective when the communication environment suffers from intermittent information, switching topology and time-delays. For the leaders, the convergence analysis can be easily obtained by using the properties of the SIA matrices. The geometric configuration of the desired formation is not affected by the switching topology or time-delays. For the followers, the convergence analysis is much complicated since the properties of the SIA matrices cannot be used. Based on the relationship between the topology and matrices, it is proved that the followers will move into the convex hull of the desired formation, and then change their positions in the convex hull as the time evolves under the switching topology; however, the final states of the followers are not affected by the time-delays. Finally, the theoretical results are illustrated by some simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the exponential leader-following consensus of multi-agent systems with high-dimensional active leader. To ensure the followers can track the leader as well as save the communication resource, a distributed observer-based controller based on periodic event-triggered mechanism is proposed. By using the delay-input method, the underlying leader-following consensus problem of multi-agent systems can be equivalently transformed into the asymptotical stability problem of the time-delay systems. Based on a novel time-delay analysis method, it is shown that the leader-following consensus can be reached. Secondly, to further reduce the amount of signal transmission, an event-triggered mechanism based on quantization is proposed. Thirdly, to remove the limitation that all followers know the system matrix of the leader system, an adaptive distributed observer-based controller is proposed. A numerical example is proposed to illustrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

In this paper, we address a formation control problem with velocity assignment of networked multi-agent systems with heterogeneous time-delays. We assume the situation that the assigned velocity is transmitted as a command signal from human operators via long-range communication. For the cost reduction, only a part of the agents, called leaders, can receive this signal. First, we show that heterogeneous time-delays cause a formation error, and derive the error in an analytic way. Second, we propose a leader selection algorithm to minimize the formation error. Here, a small number of leaders is better from the viewpoint of the cost reduction. To meet this request, we employ the LASSO (least absolute shrinkage and selection operator) which has a function of selecting as few explanatory variables as possible in optimization problems. We focus on this function of the LASSO, and consider applying it to the leader selection problem. The effectiveness of the proposed method is verified by a numerical example. [ABSTRACT FROM AUTHOR]

The paper investigates second-order consensus problem of nonlinear multi-agent systems with mixed time-delays and intermittent communications, where the mixed time-delays are composed of discrete and distributed delays, and each agent is assumed to obtain the relatively completely intermittent information of neighboring agents due to communication constraints. A new kind of distributed control protocol is designed based on the adaptive intermittent control ideas, some novel criteria are derived in matrix inequalities form by resorting to the generalized Halanay inequality. It is proved that second-order consensus can be reached if communication duration is larger than a threshold value under the strongly connected and balanced topology, and the relationship between the delays and communication duration over each control period is sought out. Finally, two simulation examples are provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem of second-order multi-agent systems with constant time-delay, fixed topology and impulsive algorithm based on periodic sampling. First, by theory of impulsive differential equations, it is proved that the consensus is achieved if and only if some matrix has a simple 1 eigenvalue and all the other eigenvalues are in the unit circle. Meanwhile, the consensus state of the system is obtained, which indicates that the positions and the velocities of all agents reach, respectively, a constant state and zero. Hence we say a static consensus is achieved for multiple second-order agents. Then, by stability of polynomials, we establish a necessary and sufficient condition from the perspective of topology and protocol parameters, which provides the range of allowable time-delay and the choice of impulse period. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the cooperative output regulation problem for linear time-delay multi-agent systems subject to jointly connected switching network. We first establish two lemmas that lay the foundation for solving the problem and then present the solution to the problem by both the dynamic state feedback control law and the dynamic measurement output feedback control law. Our results not only extend the existing results on linear multi-agent systems without time-delay to linear time-delay multi-agent systems, but also lead to the solution of the leader-following consensus problem of some typical linear time-delay multi-agent systems. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus of second-order multi-agent systems without measuring the velocity states of the agents, where each agent can be either a double integrator or a harmonic oscillator. By utilizing the position information of the agents, a distributed observer-based protocol is proposed to solve the second-order consensus problem of multi-agent systems with or without time delay. The observer-based consensus problem is converted to the stability analysis for a set of second-order quasi-polynomials through coordinate transform and system decomposition. Then, some necessary and sufficient conditions are derived for reaching second-order consensus in multi-agent systems with or without time delay, respectively, and it is shown that the consensus can be achieved if and only if the communication delay is less than a critical value. Simulation examples are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper develops a distributed secondary cooperative scheme for the current-controlled PWM inverters (CC-PWMIs) based on networked multiagent systems that can guarantee the accurate power sharing among the distributed energy resource (DER) units in microgrids. With the assumption that the communication networks are local, time-varying, and with low bandwidth, two distributed secondary controllers are designed such that all DERs in the microgrid can share their active and reactive powers accurately on the conditions of both fixed and switching topologies with time-varying communication delays. Moreover, delay-dependent sufficient conditions are obtained by using the Lyapunov–Krasovskii stable analysis method. The proposed controllers, allowing each DER unit to receive the current and active/reactive load information intermittently from its neighboring DERs, are then fully distributed. The effectiveness of the proposed control methodology is verified by the simulation of a low-voltage microgrid test system in the MATLAB/SimPowerSystems Toolbox. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics group consensus problem of heterogenous multi-agent systems with time delays, in which agents’ dynamics are modeled by single integrators and double integrators. To achieve group consensus, a class of dynamics group consensus protocols is proposed for heterogenous multi-agent systems with input time delays, which can also be used to solve group consensus for heterogenous multi-agent systems without input time delays. By using frequency-domain analysis method and matrix theory, some sufficient group consensus conditions, which are dependent on the input delays and the control parameters, are obtained for heterogenous multi-agent systems under directed and undirected communication topologies with and without input time delays, respectively. Simulation results are also provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Containment control of multi-agent system with time-delays is a meaningful topic with considerable realistic significance in the research of multi-agent systems. This paper investigates the distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders, when considering the fixed time-delay under fixed directed network topologies. In the case of studying the multi-agent delayed system with continuous-time, Laplace transform and final value theorem are employed. Specifically some sufficient conditions are obtained which can ensure the containment of the first-order multi-agent systems. Moreover, an effective control protocol is designed for the first-order discrete-time systems with fixed time-delays. Finally, simulation examples are given to verify the effectiveness of the theoretical results and conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we use the event-triggered control method to investigate the average consensus problem in distributed multi-agent systems. The communication topology among agents is characterized by an undirected and connected graph and there exist time delays in data transition. Based on local information, we give an effective delay-robust event-triggered control strategy, in which periodic event detectors are used to monitor and verify event-triggering conditions. The event-triggering condition of each agent is specified by the agent׳s own state and neighbors׳ state information, which are obtained at their respective latest event instants before event-checking instants. If the event-triggering condition is satisfied, the associated agent samples its state and updates its controller. Each agent׳s state information used in its controller is updated only at its own event times and does not need to be updated at its neighbors׳ event times, which can reduce considerably unnecessary energy expenditure. Finally, the effectiveness of our result is shown by a simulation. [ABSTRACT FROM AUTHOR]

This paper investigates cooperative tracking for nonlinear multi-agent systems, and mainly focuses on the consensus tracking subjected to one leader and containment tracking subjected to multiple leaders. Based on the outdate information stored in each agent׳s memory, a hybrid pinning protocol constructed by both current states and outdated states is proposed for consensus tracking system, which can also be viewed as a hybrid time-delayed protocol. A multi-step algorithm is then provided to construct the pinning protocol under which consensus tracking can be asymptotically solved. Furthermore, we extend the single target tracking on the network to the multi-target tracking case, i.e., containment tracking problem. Similar hybrid time-delayed protocol and multi-step algorithm can be constructed as well, which can guarantee the asymptotical containment of the nonlinear multi-agent system. It has been shown that the proposed hybrid time-delayed protocols are fairly robust to any constant time delays for the cooperative tracking problems of nonlinear multi-agent systems. Finally, some numerical examples are given to demonstrate the applicability and efficiency of the proposed schemes. [ABSTRACT FROM AUTHOR]

Lag consensus is a phenomenon where followers track the trajectory of the leader with a time delay. By using lag consensus, a protocol is designed for agents to behind the leader at different times, so as to avoid congestion. In this paper, aiming to the lag consensus of second-order nonlinear multi-agent systems, a control protocol for each follower based on local information of neighboring agents is proposed, and an adaptive feedback control protocol is also given. Moreover, the multi-agent systems with noisy environment are considered. The results suggest that our protocol is robust to the noise. Finally, simulation examples are given to illustrate our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate group consensus problems for continuous-time multi-agent systems with time delays, where the agents׳ dynamics are controlled based on information from their neighbors at some discrete time instants. By utilizing nonnegative matrix theory and graph theory, the case with fixed topology and time-invariant delays is first considered, then the general case with switching topologies and time-varying delays is discussed. Some group consensus criteria are obtained in both cases, it is also shown that the agents in nonzero in-degree groups finally converge to the convex hull of those in zero in-degree groups. Simulation examples are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the consensus problem is investigated for a group of first-order agents in the cooperation–competition network, where agents can cooperate or even compete with each other, i.e., the elements in the coupling weight matrix of the graph can be either positive or negative. In order to solve this consensus problem, the whole network is firstly divided into two sub-networks, i.e., the cooperation sub-network and the competition sub-network, and then two kinds of time-delayed control schemes are designed in the competition sub-network. By combining the Lyapunov theory together with the synchronization manifold method, several effective sufficient conditions of consensus are provided without assuming that the interaction topology is strongly connected or contains a directed spanning tree, which means that the competition relationships could help the agents achieve consensus under the time-delayed control designed in the competition sub-network. Moreover, the results are also extended to the pure competition networks where all the elements in the weight matrices are either zeros or negative. Finally, some simulation examples are provided to validate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper studies the group consensus problem of second-order multi-agent systems (MASs) with time delays. First, by state transformation method, the group consensus problem of multi-agent systems can be equivalently transformed into the asymptotical stability of a time-delay system. Then, by Lyapunov first method and Hopf bifurcation theory, respectively, we aim to find the upper bound of time delay τ ⁎ such that the multi-agent systems can achieve group consensus for τ ∈ [ 0 , τ ⁎ ) . Finally, simulation examples are given to show the effectiveness of our theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the average consensus problems of the discrete-time linear multi-agent systems (LMAS) with Markov switching topologies. The average consensus protocol is a time-delay feedback switching controller. Compared with existing controllers, it is switching with time-delay. The constant time-delay exists in the signal feedback, and the time-varying time-delay exists in the state feedback. Firstly, we introduce a concept of the average consensus in this stochastic system. Then, we develop a new signal mode to simplify this challenging problem. By Lyapunov technique, two LMIs determinate theorems of average consensus are provided. Then we can find a controller to solve such problems effectively by these theorems. And the last theorem also reveals that we can determinate consensus by the maximum and minimum nonzero eigenvalues of the Laplacian matrices. Finally, a numerical example is given to illustrate the efficiency of our results. [ABSTRACT FROM AUTHOR]

In this paper, distributed robust H ∞ rotating consensus control is investigated for a class of second-order multi-agent systems with mixed uncertainties and time-delay. Firstly, the rotating consensus is defined in the real field. To solve the consensus problem, two distributed protocols are introduced for networks with and without time-delay respectively. Then by employing Lyapunov approach and H ∞ control theory, two sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to make all agents asymptotically reach rotating consensus with the desired H ∞ performance. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a new consensus criterion for discrete-time multi-agent systems with communication-delay and disturbances. By constructing a suitable Lyapunov–Krasovskii (L–K) functional, which fractionizes the delay interval into two subsections, and utilizing reciprocally convex approach, a new consensus criterion for the concerned systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the consensus problem in directed networks with double-integrator dynamics and non-uniform time-varying communication delays. With the help of Lyapunov–Razumikhin function a necessary and sufficient condition is presented in the case when the delays are non-uniform and time-varying. Simulation results are provided to illustrate the theoretical results. [Copyright &y& Elsevier]