Robust imp ulsive synchronization of linear discrete dynamical networks

This paper aims to study robust impulsive synchronization problem for uncertain linear discrete dynamical network. For the discrete dynamical networks with unknown but bounded linear coupling ,by introducing the concept of uniformly positive definite matrix functions ,some robust impulsive controllers are designed ,which ensure that the state of a discrete dynamical network globally asymptotically synchronizes with an arbitrarily assigned state of an isolate node of the network. This paper also investigates the synchronization problem where the network coupling functions are uncertain but bounded nonlinear functions.Finally ,two examples are simulated to illustrate our results.     

复杂网络的脉冲同步

研究了具有有界耦合函数的不确定复杂动态网络的脉冲同步问题．根据脉冲控制的概念和脉冲微分方程的稳定性理论,我们利用一个灵活有效的脉冲控制实现了复杂动态网络的脉冲同步．最后,通过对混沌系统做网络节点的动态网络的数字模拟,验证了我们提出的脉冲控制方案的有效性和实用性．     

Robust synchronization of dynamical network with impulsive disturbances and uncertain parameters

In this paper, we investigate robust global exponential synchronization of an impulsive complex dynamical network with uncertain parameters. The new impulse proposed is added on the coupled states and is relative not only with the coupled states at the current impulsive time instants but also with ones at the previous impulsive time instants. Some sufficient conditions are derived to ensure robust exponential synchronization of the presented impulsive dynamical network by using the stability analysis for impulsive delay systems. The obtained results extend the existed ones. A numerical example is finally exploited to show the effectiveness of the obtained results.     

Exponential synchronization of impulsive complex networks with output coupling

This paper proposes a new impulsive complex delayed dynamical network model with output coupling, which is totally different from some existing network models. Then, by employing impulsive delay differential inequalities, some sufficient conditions are obtained to guarantee the global exponential state synchronization and output synchronization of the impulsive complex delayed dynamical network. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.     

Decentralized adaptive synchronization of an uncertain complex delayed dynamical network

In this paper, we investigate the locally and globally adaptive synchronization problem for an uncertain complex dynamical network with time-varying coupling delays based on the decentralized control. The coupling terms here are bounded by high-order polynomials with known gains that are ubiquitous in a large class of complex dynamical networks. We generalize the usual technology of searching for an appropriate coordinates transformation to change the network dynamics into a series of decoupled lower-dimensional systems. Several adaptive synchronization criteria are derived by constructing the Lyapunov-Krasovskii functional and Barbalat lemma, and the proposed criteria are simple in form and convenient for the practical engineering design. Numerical simulations illustrated by a nearest-neighbor coupling network verify the effectiveness of the proposed synchronization scheme.     

Synchronization of Uncertain Complex Networks with Time‐Varying Node Delay and Multiple Time‐Varying Coupling Delays

This paper investigates the synchronization problem of a class of complex dynamical networks via an adaptive control method. It differs from existing works in considering intrinsic delay and multiple different time‐varying coupling delays, and uncertain couplings. A simple approach is used to linearize the uncertainties with the norm‐bounded condition. Simple but suitable adaptive controllers are designed to drive all nodes of the complex network locally and globally synchronize to a desired state. In addition, several synchronization protocols are deduced in detail by virtue of Lyapunov stability theory and a Cauchy matrix inequality. Finally, a simulation example is presented, in which the dynamics of each node are time‐varying delayed Chua chaotic systems, to demonstrate the effectiveness of the proposed adaptive method.     

Stochastic synchronization of delayed multiagent networks with intermittent communications: An impulsive framework

This paper investigates the stochastic synchronization problem of delayed multiagent networks with intermittent communications. Two kinds of impulsive effects are taken into account, ie, impulsive controller (positive impulsive effect) and impulsive disturbance (negative impulsive effect). Impulsive controller allows the synchronization to be realized and requires only state information exchange at discrete time instants such that the communication cost of bandwidth is reduced. Meanwhile, impulsive disturbance is inevitable in most of practical systems and therefore is taken into consideration at discrete time instants. Sufficient conditions for synchronization are given in terms of the graph topology, the control coupling gains, and the individual agent dynamics parameters, which indicates that synchronization can be realized if the impulsive effects coefficients and communication rate are suitably selected. Simulation results verify the effectiveness of the proposed synchronization protocol.     

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

This paper is concerned with the problem of synchronization of complex dynamical networks with state and coupling time‐delays. Therefore, larger class and more complicated complex dynamical networks could be considered for the synchronization problem. Based on the Lyapunov‐Krasovskii functional, some delay‐independent and delay‐dependent criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the synchronization between each node of the complex dynamical network. The effectiveness of the proposed method is illustrated using some numerical simulations.     

Distributed impulsive synchronization of Lur'e dynamical networks via parameter variation methods

This paper is devoted to investigating the exponential synchronization of coupled Lur'e dynamical networks with multiple time‐varying delays and stochastic disturbance. The problem studied in this paper could be regarded as a kind of leader‐following synchronization issue. As the networks may suffer from certain impulsive disturbance, an effective distributed impulsive control protocol is proposed to synchronize the stochastic Lur'e dynamical networks. According to the comparison principle, the average impulsive interval, and the extended formula for the variation of parameters, sufficient conditions are derived for successful achievement of the network synchronization with consideration to different functions of impulsive effects. Furthermore, the exponential convergence rate is obtained based on the impulsive solution equation. In addition, finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis.     

H∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

In this paper, robust H_∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H_∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.     

具有脉冲耦合复杂时滞动力网络的同步

考虑了一个具有脉冲耦合的复杂时滞动力网络的同步问题.基于脉冲时滞动力系统扩展的Halanay不等式,给出了网络同步的一个充分条件.所获结果表明,即使网络节点之间仅在一些离散时刻存在瞬时连接,网络仍然能够达到同步.进一步将所得结果应用于一个由混沌FHN神经元振子为动力节点所构成的一个无标度的动力网络,数值仿真结果表明了理...     

时变复杂动力学网络的同步控制

研究时变复杂动力学网络的同步控制问题.假定网络模型中的同步轨迹及耦合配置矩阵、内部耦合矩阵的各元素均有界,当这些界值可以预估或不确定时,分别应用线性反馈控制和自适应反馈控制策略使该网络实现全局同步.通过构造Lyapunov函数,证明了对于任意初始状态的时变复杂动力学网络模型在相应的控制手段下总可以实现渐近同步.特别是设计的自适应反馈控制策略对网络的拓扑结构、节点间的耦合强度及时滞等因素表现出较强的鲁棒性.数值仿真证实了上述结论的有效性.     

Optimal control and robust stability of uncertain impulsive dynamical systems

This paper studies the problem of optimal feedback control and robust stability for uncertain impulsive dynamical systems. By using algebraic inequalities, Riccati and Hamilton‐Jacobi inequalities, the conditions are derived under which not only the uncertain impulsive dynamical system has robust asymptotic stability but also the value of the optimal hybrid performance functional can be estimated. An example is also given to illustrate our results. © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H∞ control of uncertain linear impulsive stochastic systems

This paper develops robust stability theorems and robust H_∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous‐time stochastic dynamics and unstable/unstabilizable discrete‐time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete‐time dynamics, and the systems in which both the continuous‐time stochastic dynamics and the discrete‐time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell‐time condition. Then, a linear matrix inequality‐based approach to the design of a robust H_∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

具有量化脉冲效应的时滞混杂动态网络同步分析

研究了具有量化脉冲效应的时滞混杂动态网络的同步动力学,利用偏收缩理论和矩阵测度概念,并结合量化器的特征,提出了网络节点实现同步的一般性条件.与以往大多数基于Lyapunov稳定性方法所提出的结果不同,利用本文的方法可以消除单个节点和网络耦合中的非线性函数的限制性假设,从而降低保守性.本文突出的特征就是综合了网络节点和耦合拓扑中的多重时滞影响和脉冲行为,并且考虑了脉冲效应在网络传输中的有限通信能力问题,具有实际意义.最后,通过对Lorenz混沌系统作为网络节点的混杂动态网络进行数值模拟,验证了所得结果的有效性.     

基于线性反馈控制器的时变时滞动态网络中的同步

主要研究具有时变时滞的动态复杂网络中的同步问题. 考虑两种时变时滞的情况—时滞连续一致有界和时滞可微且导数一致有界. 这里假设耦合结构矩阵非对称并且可约. 提出一些新的时滞相关的同步准则并且利用线性状态反馈控制器得到一些同步控制的结果, 其中控制器可以由Matlab软件求得. 最后给出一些数值仿真例子以说明同步准则的有效性.     

Adaptive stabilizing state feedback controllers of uncertaindynamical systems with multiple time delays

The problem of robust stabilization for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, it is assumed that each perturbation is bounded by a linear function of delayed state with unknown gains, and an adaptation law is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes is globally stable in the sense of uniform ultimate boundedness. Finally, a numerical example is given to demonstrate the validity of the results     

Linear quadratic networked control of uncertain polytopic systems

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous‐time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete‐time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete‐time domain assures a guaranteed quadratic cost to the closed‐loop continuous‐time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete‐time domain, a digital robust state feedback control law that stabilizes the original continuous‐time system assuring an upper bound to the quadratic cost of the closed‐loop system. The applicability of the proposed design method is illustrated through a numerical experiment. Copyright © 2015 John Wiley & Sons, Ltd.     

2-D奇异系统Roesser模型的鲁棒H∞控制

考虑具有参数不确定性的2-D奇异系统Roesser模型(简称2-D SRM)鲁棒H∞控制问题．在给出界实引理的另一等价形式的基础上,通过求解矩阵不等式,给出了不确定2-D奇异系统鲁棒H∞控制问题可解的充分条件及静态状态反馈控制律设计的代数表达式．最后通过一个仿真算例验证了方法的有效性．     

复杂动力学网络的自适应线性广义同步及参数识别

针对参数未知的复杂动力学网络，基于Lyapunov稳定性理论和LaSMle不变原理，通过设计合适的自适应控制器不仅实现了参数未知的复杂动力学网络之间的线性广义同步，而且对网络中的未知参数进行了追踪识别．文中设计的控制器对一类复杂动力学网络有普适性，并且由于其具有的自适应功能，使得该控制方法有鲁棒性．数值仿真结果进一步验证了控制方法的有效性与可行性．