不确定时滞Lurie型控制系统与时滞相关的绝对稳定性

研究了一类参数不确定的具有多个时滞的Lur′e型控制系统与时滞相关绝对稳定性问题.通过将原系统变换为等价的奇异系统,利用Moon不等式放大向量积,构造出一个新的Lyapunov-Krasovskii泛函.并由此基于线性矩阵不等式,得到了系统与时滞相关绝对稳定的充分条件.这些充分条件无须预调任何参数矩阵,可以直接运用Matlab软件中LMI工具箱求解.数值例子表明,与现有结果相比,本文结果较大地改进了保证不确定时滞Lur′e型控制系统绝对稳定的时滞界.     

基于一般Lur''''e系统的混沌同步研究

许多混沌系统可以转化为一个Lur'e系统.本文采用时滞反馈控制技术研究了一般Lur’e系统的混沌同步问题,改进了最近有关文献的结果.通过利用Lyapunov—Krasovskii函数法得到了时滞无关的线性矩阵不等式(LMI)判据,而且还通过利用M-矩阵等方法,得到了易于检验的时滞相关与时滞无关的代数判据,利用这些结果给出了这种反馈控制器的设计方法;最后,给出的例子阐明了所得到的结果.     

时滞输出反馈非恒同主从耦合混沌系统一致同步的判据

当主从耦合混沌系统的参数之间非恒同时,一般意义上的混沌同步难以实现,因此,讨论了其具有一定误差界的一致同步问题.本文对一类包含Lur’e系统和Lipschitz系统在内的混沌系统,应用Lyapunov函数方法导出通过时滞输出反馈控制实现一致同步的充分条件,该判据用矩阵不等式的形式给出.进而讨论了同步的鲁棒性问题.最后结合Chua电路对结论进行了数值模拟,验证了结论的正确性与有效性.     

主从Lur’e系统混沌同步的时滞输出反馈控制

该文讨论了主从Lur’e系统之间混沌同步的输出反馈控制问题,利用Lyapunov方法和矩阵不等式技巧,得到了一个依赖于时滞的混沌同步的充分条件,该条件易于用LMI(线性矩阵不等式)方法进行验证,并可对最大允许时滞进行估计,最后结合Chua’s电路进行了数值模拟。     

时变时滞Lurie非线性系统绝对稳定新判据

针对时变时滞Lurie非线性系统,应用增广Lyapunov-Krasovskii泛函结合自由权矩阵方法,研究其时滞相关绝对稳定性问题.通过保留Lyapunov-Krasovskii泛函导数中常被忽略的有用信息,充分考虑时变时滞、时滞上界及它们的差三者之间的关系,得到了具有更低保守性的基于线性矩阵不等式的时滞相关绝对稳定条件.数值实例表明,该方法得出的结果优于已有文献的结果.     

基于间歇控制的不确定主从Lur’e系统的指数同步

研究了不确定主从Lur’e系统的问歇控制同步问题．运用Lyapunov稳定性理论和S-过程,首先推导出保证标称主从Lur’e系统指数同步的一个充分条件．在此基础上进一步得到了具有范数有界不确定性主从Lur’e系统鲁棒指数同步的结果．这些同步判据以矩阵不等式的形式给出．另外我们还提出了一种最小化性能指标的优化策略．最后,通过两个数值例子验证了结果的有效性．     

一类时滞矩形广义系统的镇定

为研究时滞矩形广义系统的镇定问题,首先引入时滞动态补偿器对系统进行反馈补偿,然后构建一个合适的Lyapunov-Krasovskii泛函,并选取先进的积分不等式来处理泛函导数的积分项,进而获得了以严格线性矩阵不等式(LMI)表示的时滞矩形广义系统的镇定条件。在此基础上,利用迭代线性矩阵不等式的算法计算动态补偿器和反馈增益的参数矩阵。最后,通过数值算例验证了方法的有效性和优越性。     

关联大系统时变时滞状态反馈分散鲁棒H∞控制

设计了分散状态反馈H∞控制器,引入一种积分不等式方法,结合Lyapunov-Krasovskii泛函方法和积分矩阵不等式技巧导出了此类系统的时滞分散H∞控制的非线性矩阵不等式(NMI)充分条件.使用改进的锥补法(CCL)导出了此类系统时滞分散H∞控制的线性矩阵不等式(LMIs)充分条件.     

带有非线性扰动的时变时滞系统的稳定性准则

研究了带有非线性扰动的时变时滞系统的稳定性问题.基于时滞分割方法,提出了保守性更小的系统稳定性分析准则.利用一个自由参数将时滞区间分割为2个子区间,进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函,并采用自由矩阵积分不等式界定泛函导数中的交叉项.基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则.数值算例表明该稳定性准则能够得到更大的时滞上界,与已有结果相比具有更小的保守性.     

多胞不确定型多时变时滞系统的稳定性

采用积分等式方法处理Lyapunov-Krasovskii泛函导数中的交叉项, 利用牛顿–莱布尼兹公式和自由权矩阵来保留状态的导数项, 标称系统的稳定性条件中的系统矩阵和Lyapunov矩阵得以分离, 再通过参数依赖Lyapunov-Krasovskii泛函得到多胞不确定型系统的鲁棒稳定性结论, 最后数值算例说明稳定性条件的有效性.     

奇异Lur'e网络的自适应牵制聚类同步控制

本文分别研究了由奇异和非奇异Lur''e系统组成的具有多种耦合方式时滞复杂动态网络的聚类同步问题. 通过设计一类牵制反馈控制器, 仅控制当前聚类中与其它聚类有直接连接的Lur''e系统, 从而有效减少控制器个数同时降低控制成本. 考虑到网络具有多种耦合方式, 本文合理构造Lyapunov 泛函, 并有效利用扇形条件、非线性函数类概念、S过程以及Lyapunov 稳定性定理等方法, 分别给出奇异和非奇异Lur''e 动态网络实现聚类同步的判定条件. 此外, 为有效节省控制成本, 针对控制强度设计一类自适应更新定律, 从而得到网络实现聚类同步的最优控制强度. 最后, 为了验证所得聚类同步判定条件和控制器的有效性, 对一类典型Lur''e网络聚类同步问题进行了数值仿真.     

Memory feedback PID control for exponential synchronisation of chaotic Lur'e systems

This paper studies the problem of exponential synchronisation of chaotic Lur'e systems (CLSs) via memory feedback proportional-integral-derivative (PID) control scheme. First, a novel augmented Lyapunov–Krasovskii functional (LKF) is constructed, which can make full use of the information on time delay and activation function. Second, improved synchronisation criteria are obtained by using new integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. In comparison with existing results, in which only proportional control or proportional derivative (PD) control is used, less conservative results are derived for CLSs by PID control. Third, the desired memory feedback controllers are designed in terms of the solution to linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results.     

New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.     

Synchronization Criterion and Control Scheme for Lur'e Type Complex Dynamical Networks with Switching Topology and Coupling Time‐Varying Delay

In this paper, the synchronization problem is addressed in the context of Lur'e type complex switched network (CSN) with coupling time‐varying delay in which every node is a Lur'e system. Based on the Lyapunov–Krasovskii theory and linear matrix inequality (LMI) technique, a delay‐dependent synchronization criterion and a decentralized state feedback dynamic controller for synchronization of CSNs have been proposed. By choosing a common Lyapunov–Krasovskii functional and using the combined reciprocal convex technique, some previously ignored terms can be reconsidered and less conservative conditions can be obtained. In addition, by using an eigenvalue‐decoupling method and convex optimization theory, high‐dimension LMIs are decoupled into a set of low‐dimension ones and the computation complexity of the criterion can be significantly reduced. The effectiveness and applicability of the suggested control solution is verified and assessed through the analysis for two numerical examples.     

Master‐slave synchronization for delayed Lur'e systems using time‐delay feedback control

This paper deals with the problem of designing delayed feedback controllers of master‐slave synchronization for Lur'e systems with time‐variant delay (0≤τ₀≤τ(t)≤τ_m). Through partitioning the intervals [0, τ₀] and [τ₀, τ_m], respectively, and choosing two augmented Lyapunov‐Krasovskii functionals(LKFs), two delay‐dependent synchronization criteria are formulated in the form of linear matrix inequalities (LMIs), in which the conservatism can be greatly reduced by thinning the partitioning of delay intervals and employing convex combination. Thus the sufficient conditions can be derived for the existence of delayed feedback controllers, and the controller gain matrices can be achieved by solving the established LMIs. Finally, three numerical examples are given to illustrate the presented synchronization schemes. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Improved robust stability criteria for a class of Lur'e systems with interval time-varying delays and sector-bounded nonlinearity

This paper is concerned with the absolute and robust stability for a class of neutral-type Lur'e systems with an interval time-varying delay and sector-bounded nonlinearity. By discretising the delay interval into two segmentations with an unequal width, new delay-dependent sufficient conditions for the absolute and robust stability of neutral-type Lur'e systems are proposed in terms of linear matrix inequalities (LMIs) by employing a modified Lyapunov-Krasovskii functional (LKF). These conditions reduce the conservativeness in computing the maximum allowed delay bounds (MADBs) in many cases. Finally, several standard numerical examples are presented to show the effectiveness of the proposed approach.     

On Designing Time‐delay Feedback Controller for Master‐Slave Synchronization of Lur'e Systems

This paper is concerned with the problem of designing a time‐delay output feedback controller for master‐slave synchronization of Lur'e systems. The time delay is divided into two intervals and different energy functions are defined in each interval, which together provide a new Lyapunov–Krasovskii functional and derive a new delay‐dependent synchronization criterion. A sufficient condition for the existence of such a feedback controller is given, and an explicit expression of such a controller is also achieved. These algorithms are formulated in terms of linear matrix inequalities that can be solved easily. Chua's circuit is used to illustrate the effectiveness of the design method.     

Lur'e Lyapunov functions and absolute stability criteria for Lur'e systems with multiple nonlinearities

In this paper, the absolute stability problem of Lur'e systems with multiple nonlinearities is investigated. Popov‐type absolute stability criteria are surveyed and classified by distinguishing the Lur'e Lyapunov function upon which the criteria are based. A modified Lur'e Lyapunov function is presented. Some necessary and sufficient conditions for the existence of the Lyapynov function to guarantee the absolute stability of Lur'e systems are derived. By these conditions, LMI‐based stability criteria are presented. The obtained criteria are expected to be less conservative than the existing ones. Finally, numerical examples are given to illustrate the advantages and effectiveness of our results. Copyright © 2006 John Wiley & Sons, Ltd.     

Homogeneous control law design for output synchronization of networked Lur'e‐type systems with disturbances

In this paper, the homogeneous distributed control law is proposed such that the outputs of the networked Lur'e systems with disturbances are synchronized. A novel adaptive distributed state‐based disturbance compensator technique is utilized such that the disturbances can be offset asymptotically. The design of the distributed compensator is constructive in that some particular functions of the states of the Lur'e systems are included. The functions always exist for the considered Lur'e‐type system. Moreover, a theorem of networked Lur'e systems subject to disturbances is first presented to show the boundedness of the states of the closed‐loop system. Then, the synchronization is shown by the incremental passivity theory and graph theory. Finally, the effectiveness of the current method is illustrated by the networked Van der Pol oscillators with disturbances.     

Global synchronised regions of linearly coupled Lur'e systems

This article addresses the global synchronisation problem of a network of coupled Lur'e systems from the perspective of global synchronised region. A decomposition approach is proposed to convert the synchronisation of high-dimensional Lur'e networks into the test of a set of matrix inequalities whose dimensions are the same as a single Lur'e node. The notion of global synchronised region is then introduced and analysed. A necessary and sufficient condition is derived for the existence of the inner-linking matrix to guarantee a desirable unbounded synchronised region. A multi-step design procedure is given for constructing such an inner-linking matrix, which maintains a favourable decoupling property. Furthermore, the global H _∞ synchronised region is characterised for evaluating the performance of a Lur'e network subject to external disturbances. The effectiveness of the theoretical results is demonstrated through a network of Chua's circuits.