State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: The discrete-time case

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the synchronization control problem is considered for two coupled discrete-time complex networks with time delays. The network under investigation is quite general to reflect the reality, where the state delays are allowed to be time varying with given lower and upper bounds, and the stochastic disturbances are assumed to be Brownian motions that affect not only the network coupling but also the overall networks. By utilizing the Lyapunov functional method combined with linear matrix inequality (LMI) techniques, we obtain several sufficient delay-dependent conditions that ensure the coupled networks to be globally exponentially synchronized in the mean square. A control law is designed to synchronize the addressed coupled complex networks in terms of certain LMIs that can be readily solved using the Matlab LMI toolbox. Two numerical examples are presented to show the validity of our theoretical analysis results.This work was supported by the Royal Society Sino-British Fellowship Trust Award of the U.K

Robust adaptive synchronization of dynamic networks with varying time delay coupling using varible structure control

The synchronization problem for a class of delayed complex dynamical networks via employing variable structure control has been explored and a solution proposed. The synchronization controller guarantees the state of the dynamical network is globally asymptotically synchronized to arbitrary state. The switching surface has been designed via the left eigenvector function of the system, and assures the synchronization sliding mode possesses stability. The hitting condition and the adaptive law for estimating the unknown network parameters have been used for designing the controller hence the network state hits the switching manifold in finite time. Two illustrative examples along with the respective simulation results are given, which employ the designed variable structure controllers

Exponential synchronization of complex delayed dynamical networks with general topology

The global exponential synchronization of complex delayed dynamical networks possessing general topology is investigated in this contribution. The network model considered can represent both the directed and undirected weighted networks. Novel delay-dependent linear controllers are designed via Lyapunov stability theory and appropriate property of the coupling matrix. It is shown that the controlled network is globally exponentially synchronized with a given convergence rate. Two examples of typical dynamical networks with coupling delays of this class, one possesses directed and the other with undirected coupling topology, both having a Lorenz system at each node, have been used to demonstrate and verify the novel control design proposed. © 2007 IEEE.published_or_final_versio

Synchronisation of linear continuous multi-agent systems with switching topology and communication delay

A distributed dynamic output feedback control is designed by Scardovi and Sepulchre for the synchronization of a network of identical linear systems, known as agents in literature. The design is based on some mild conditions allowing switching topology. But it assumes that there is no time delay in signal transfer between the neighbouring agents. In this paper we extend their work to include known time delay in communications. Furthermore, our design has some special features: (a) the delay can be arbitrary and only need to be uniformly bounded by a constant, (b) the conditions that time delay should be the same and sufficiently small in some literature are not required here, and (c) no local buffer is required to store past data due to time-delay effect

Stability analysis and H ∞ control for hybrid complex dynamical networks with coupling delays

This paper formulates and studies a model of complex dynamical networks with switching topology and coupling delays. Based on the hybrid control and Lyapunov function, the stability and robust H control of such networks with impulsive and switching effects, which have not been studied before, are addressed with some criteria derived. Examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd

Exponential Synchronization of Complex Delayed Dynamical Networks With Switching Topology

This paper studies the local and global exponential synchronization of a complex dynamical network with switching topology and time-varying coupling delays. By using stability theory of switched systems and the network topology, the synchronization of such a network under some special switching signals is investigated. Firstly, under the assumption that all subnetworks are self-synchronizing, a delay-dependent sufficient condition is given in terms of linear matrix inequalities, which guarantees the solvability of the local synchronization problem under an average dwell time scheme. Then this result is extended to the situation that not all subnetworks are self-synchronizing. For the latter case, in addition to average dwell time, an extra condition on the ratio of the total activation time of self-synchronizing and nonsynchronizing subnetworks is needed to achieve synchronization of the entire switched network. The global synchronization of a network whose isolate dynamics is of a particular form is also studied. Three different examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results. © 2006 IEEE.published_or_final_versio

Clustering in diffusively coupled networks

This paper shows how different mechanisms may lead to clustering behavior in connected networks consisting of diffusively coupled agents. In contrast to the widely studied synchronization processes, in which the states of all the coupled agents converge to the same value asymptotically, in the cluster synchronization problem studied in this paper, we require all the interconnected agents to evolve into several clusters and each agent only to synchronize within its cluster. The first mechanism is that agents have different self-dynamics, and those agents having the same self-dynamics may evolve into the same cluster. When the agents' self-dynamics are identical, we present two other mechanisms under which cluster synchronization might be achieved. One is the presence of delays and the other is the existence of both positive and negative couplings between the agents. Some sufficient and/or necessary conditions are constructed to guarantee n-cluster synchronization. Simulation results are presented to illustrate the effectiveness of the theoretical analysis. (C) 2011 Elsevier Ltd. All rights reserved