Explicit condition for consensus of third-order discrete-time multi-agent systems without accelerated velocity measurements

This paper investigates the consensus problem for third-order discrete-time multi-agent systems in directed networks. For the case when each agent can only receive the information of position and velocity from its neighbors, necessary and sufficient conditions for consensus have been proposed. In contrast to the preceding work, we not only present the exact consensus value, but also illustrate the influence of scaling parameters and nonzero eigenvalues of the involved Laplacian matrix on consensus. Two numerical examples are given to demonstrate the effectiveness of the obtained results.     

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Matrix-weighted consensus for multi-agent systems with sampled-data

This paper researches the consensus issue for multi-agent systems on matrix-weighted directed fixed and undirected switching network topologies by sampled data control method which saves resources and is more practical. Using the sampled information, the distributed control laws are designed under two network topologies, respectively. Under directed fixed network topology, the consensus conditions based on the sampling period and the eigenvalues of Laplacian matrix are deduced by matrix theory and analysis theory. Under undirected switching network topology, by using Lyapunov stability theory, the consensus conditions based on the sampling period and switched network topologies are built. Lastly, two simulation examples are offered to verify the validity of the obtained results.     

Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and Markovian switching topologies

This paper studies the event-based consensus problem of second-order multi-agent systems with actuator saturation under fixed topology and Markovian switching topologies. By a model transformation, the consensus problem is first converted into the stability problem of the error system. Using discontinuous Lyapunov functional approach, two sufficient conditions on the consensus are derived for second-order multi-agent systems with fixed topology and Markovian switching topologies, respectively. The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay, and thus lead to a less conservative consensus criterion. It is shown that the consensus condition depends on the parameters of sampling period, Laplacian matrix, and event-triggered parameter. In addition, this paper provides an effective method to co-design both the consensus controller and the event-triggered parameter. Finally, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed algorithm.     

Leader-following successive lag consensus of nonlinear multi-agent systems via observer-based event-triggered control

This article investigates the leader-following successive lag consensus (SLC) for nonlinear multi-agent systems (NMASs) via the observer-based event-triggered control (OBETC), in which two scenarios including constant consensus delay and time-varying consensus delay are considered. Since the system states might not be directly available in actual scenes, the state estimation method is utilized for followers to track their full information. Based on the relative state, a class of distributed event-triggered control protocols is constructed, where the event-triggered strategy is introduced such that each follower can determine the broadcasting time to its neighbors. Obviously, these designed control protocols considerably lessen the expense over communication networks and the frequency of protocol updates. Furthermore, with the aid of the Lyapunov function method, a series of sufficient conditions for guaranteeing the leader-following SLC of NMASs is obtained. Meanwhile, it is proved that no Zeno behavior is exhibited. Finally, several numerical examples are given to illustrate the validity of our theoretical results.     

Average consensus in networks of dynamic agents with uncertain topologies and time-varying delays

In this paper, we study average consensus problem in networks of dynamic agents with uncertain topologies as well as time-varying communication delays. By using the linear matrix inequality method, we establish several sufficient conditions for average consensus in the existence of both uncertainties and delays. Several linear matrix inequality conditions are presented to determine the allowable upper bounds of time-varying communication delays and uncertainties. Numerical examples are worked out to illustrate the theoretical results.     

Mean-square consensus of hybrid multi-agent systems with noise and nonlinear terms over jointly connected topologies

This paper studies the mean-square consensus of second-order hybrid multi-agent systems over jointly connected topologies. Systems with time-varying delay and multiplicative noise are considered. The date sampling control technique is adopted. Through matrix transformation, a positive definite matrix transformed by the Laplacian matrix is obtained, where the Laplacian matrix is a connected subgraph divided by the jointly connected topologies. By using graph theory, matrix theory and Lyapunov stability theory, sufficient conditions and the upper bound of time delays for the mean-square consensus are obtained. Finally, several simulations are presented to demonstrate the validity of the control method.     

Stability analysis for switched genetic regulatory networks: An average dwell time approach

In this correspondence, the problem of exponential stability for switched genetic regulatory networks (GRNs) with time delays is investigated. The GRNs are composed of N modes and the network switches from one mode to another. By employing the piecewise Lyapunov functional method combined with the average dwell time approach and by using a novel Lyapunov–Krasovskii functional (LKF), sufficient criteria are given to ensure the exponential stability for the switched GRNs with constant and time-varying delays, respectively. These criteria are proved to be much less conservative than the most recent results, since the results reported in this paper not only depend on the delay bounds, but also depend on the partitioning. All the conditions presented here are in the form of matrix inequalities which are easy to be verified via the Matlab toolbox. Two examples are provided in the end of this paper to illustrate the effectiveness of the obtained theoretical results.     

Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results.     

Fractional-order follower observer design for tracking consensus in second-order leader multi-agent systems: Periodic sampled-based event-triggered control

This paper investigates the tracking consensus problem for the second-order leader systems by designing fractional-order observer, where a periodic sampled-based data event-triggered control is employed. In order to track the position information of leader, observers for followers are designed by fractional-order system, where only the relative position information is available. Furthermore, in the process of observers design, a sampled-based event-triggered strategy is proposed so that observers use the event-triggered sampled-data, to reduce the overall load of the network. In our proposed event-triggered strategy, the event detection only works at every sampling time instant which determines whether the sampled-data should be discarded or used. Under this control strategy, the Zeno-behavior is absolutely excluded since the minimum of inter-event times is inherently lower bounded by one sampling period. It is found that the followers can track state of the leader if fractional-order observers are appropriately designed and relevant parameters are properly selected. By using the generalized Nyquist stability criterion, a necessary and sufficient condition for the observer tracking consensus of the second-order leader systems is derived. The results show that the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix, and fractional-order α of observer play a vital role in reaching consensus.     

Predefined-time practical consensus for multi-agent systems via event-triggered control

This paper studies the predefined-time practical consensus problem for multiple single-integrator systems through event-triggered control. A new kind of time-varying functions is firstly proposed. Then, new event-triggered control inputs as well as triggering conditions are designed on the basis of the time-varying function and the local broadcasted states. In particular, the control scheme is fully-distributed because no global information of the system and the communication topology is needed. Furthermore, the consensus analysis is presented based on a sufficient condition for predefined-time practical stability. It illustrates that practical consensus can be ensured with a completely pre-specified time. Besides, the exclusion of Zeno behavior at all the time instants is addressed. Numerical results verify the validity of the obtained control method.     

Global dissipativity of delayed neural networks with impulses

In this paper, we investigate the problem of global exponential dissipativity of neural networks with variable delays and impulses. The impulses are classified into three classes: input disturbances, stabilizing and “neutral” type—the impulses are neither helpful for stabilizing nor destabilizing the neural networks. We handle the three types of impulses in a uniform way by using the excellent ideology introduced recently. To this end, we propose new techniques which coupled with more general Lyapunov functions to realize the ideology and it is shown that they are more effective. Exponential dissipativity conditions are established in terms of linear matrix inequalities (LMIs) and these conditions can be straightforwardly reduced to exponential stability conditions. Numerical results are given to show that the obtained conditions are effective and less conservative than the existing ones.     

On consensus control of nonlinear multiagent systems satisfying incremental quadratic constraints

In this paper, we investigate the problem of leaderless consensus control for the multiagent systems whose nonlinear dynamics satisfying incremental quadratic constraints. A distributed dynamic consensus protocol, decided by communication among neighboring agents, is presented to render nonlinear agent consensus with appropriate coupling weights. Next, an observer-based distributed protocol is considered to ensure consensus of nonlinear system without knowing full state information. Further, extensions to consensus strategies with nonlinear dynamics for the leader-following fashion are also addressed. By comparison to the traditional nonlinear consensus control methodologies, the proposed approach generalizes the Lipschitz nonlinearity as well as the combined nonlinearity of one-sided Lipschitz condition and quadratic inner-boundness condition towards a more generalized type of nonlinearity, which shows us a less conservative result in the Lyapunov proof. Finally, the numerical simulations for six agents are illustrated to show the feasibility and performance of the proposed control protocol with or without the presence of the observer.     

Delay-dependent exponential stability for a class of neural networks with time delays and reaction-diffusion terms

In this paper, the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type has been studied. By constructing appropriate Lyapunov functional and using the linear matrix inequality (LMI) optimization approach, a series of sufficient criteria is obtained ensuring the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks. These conditions are dependent on the size of the time delay and the measure of the space, which is usually less conservative than delay-independent and space-independent ones. And, these networks are generalized without assuming the boundedness and differentiability of the activate functions. The proposed LMI condition can be checked easily by recently developed algorithms. The results are new and improve the earlier work. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations

In this paper, we discuss the properties of the eigenvalues related to the symmetric positive definite matrices. Several new results are established to express the structures and bounds of the eigenvalues. Using these results, a family of iterative algorithms are presented for the matrix equation AX=F and the coupled Sylvester matrix equations. The analysis shows that the iterative solutions given by the least squares based iterative algorithms converge to their true values for any initial conditions. The effectiveness of the proposed iterative algorithm is illustrated by a numerical example.     

Merging relative sensing networks: A stability margin perspective

This study considers merging dynamical networks (relative sensing networks in this paper) in terms of a stability margin criterion. The main motivation of this consideration is that merging can cause a significant drop in the stability margin of merged network with respect to the original networks initially with ample stability margins. In this paper, various types of network merging (i.e. undirected/directed homogeneous/heterogeneous dynamical network merging via one-way/two-way links) are analysed to show their effects on the stability margin. In particular, it is shown that (1) merging with one-way links yields the stability margin less than the original networks’; (2) merging undirected homogeneous networks with two-way links results in a stability margin being at least a quantity solely characterized by the positive realness (PRness) of SISO (Single-Input-Single-Output) local dynamics; (3) the quantity depends both on the PRness of SISO local dynamics and the eigenvalues of Laplacian matrix, in case of merging directed homogeneous networks with two-way links; (4) two-way merging using multiple nodes may allow for a large increase in the stability margin; and (5) merging heterogeneous networks may be simply treated as merging homogeneous networks by exploiting the design of link dynamics. Several numerical results are presented to show their consistency with the performed analysis.     

Fixed-time bipartite consensus of nonlinear multi-agent systems under directed signed graphs with disturbances

This paper considers the fixed-time bipartite consensus of nonlinear multi-agent systems (MASs) subjected to external disturbances. Under the directed signed networks, several sufficient conditions are proposed to guarantee the fixed-time bipartite consensus of MASs with or without leaders, respectively. Some discontinuous control protocols are developed to realize fixed-time tracking bipartite consensus of MASs with a leader. Moreover, the fixed-time leaderless bipartite consensus under directed signed graph are discussed as well. Two numerical examples are given to verify the effectiveness of the theoretical results.     

Distributed tracking control of second-order multi-agent systems with sampled data

This paper studies the leader–follower consensus problem of second-order multi-agent dynamical systems with fixed and stochastic switching topologies in a sampled-data setting. A distributed linear consensus protocol is designed to track an active leader, where the current position information of neighbor agents and self-velocity data are utilized. A necessary and sufficient condition is established under fixed and directed topology for reaching consensus, which depends on the sampling period and control gain parameters. A sufficient condition is obtained under the Markov switching topology case. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.     

Stability analysis of stochastic fuzzy Markovian jumping neural networks with leakage delay under impulsive perturbations

This paper investigates the global asymptotic stability of stochastic fuzzy Markovian jumping neural networks with mixed delays under impulsive perturbations in mean square. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delay and continuously distributed delay. By using the Lyapunov functional method, reciprocal convex approach, linear convex combination technique, Jensen integral inequality and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.