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.     

一类改进混沌Lur'e系统的滞后同步判据

本文研究了混沌Lur′e系统的滞后同步问题.通过合理构造增广Lyapunov-Krasovskii泛函,使得增广向量不仅包括单积分项以及双积分项,而且加入了增广的三重积分项.在估计Lyapunov-Krasovskii泛函导数表达式的基础上,通过零等式引入自由矩阵,同时利用积分不等式,求得以线性矩阵不等式形式表达下的混沌Lur′e系统滞后同步的判据,即充分条件.最后,通过数值计算表明本文理论研究的有效性.     

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.     

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.     

变结构控制实现非线性系统的输出调节和鲁棒输出调节

对于确定性的和受到结构扰动的非线性系统，用变结构控制设计的控制律能够满足到达条件，构造的切换面能产生稳定的滑动模态。当非线性系统在切换面上运动时，可以实现输出调节和鲁棒输出调节。     

参数化不确定非线性系统的鲁棒控制

首次用鲁棒控制的方法解决参数化反馈型非线性系统的输出调节问题,利用递推方法设计了鲁棒控制器。所得控制器既能保证所有闭环系统信号的全局有界性,又能使闭环系统输出任意小,其一大优点是能对闭环系统的过渡响应进行分析。     

Stability analysis and controller design for Lur'e system with hysteresis nonlinearities: a negative-imaginary theory based approach

In this paper, absolute stability condition is investigated when a hysteresis nonlinearity is connected to a linear subsystem via positive feedback in Lur'e system framework. In particular, the nonlinearity is considered to belong to the time-invariant slope-restricted counter-clockwise hysteresis class. An absolute stability criterion is proposed in terms of the negative-imaginary system properties. In effect, the stability condition requires the linear subsystem to belong to the strongly strict negative-imaginary (SSNI) system class along with satisfying a matrix condition involving the DC-gain of the linear subsystem and the slope-upper-bounds of the nonlinearities. Compliance to the conditions guarantees asymptotic convergence of state-trajectories to an equilibrium set. Invoking the stability result and exploiting the relaxed minimality assumption of SSNI systems, a static state-feedback synthesis method is proposed to ensure absolute stability for such hysteretic systems. Tractable conditions in the form of linear matrix inequalities can be solved to obtain a stabilising state-feedback gain matrix. Finally, a numerical example of multi-input–multi-output system is presented to illustrate the usefulness of the proposed results.     

有限时间内异构多智能体系统的协同输出调节

针对异构多智能体系统有限时间输出调节问题,本文提出了分布式有限时间状态观测器控制算法和相应的输出反馈控制策略.应用图论、Lyapunov稳定性理论证明了所设计的观测器能够在有限时间内估计出外部系统状态,同时可以保证系统在有限时间内的稳定性,很好的解决了当部分跟随者无法获取外部命令时的有限时间输出调节问题.最后,通过MATLAB数值仿真验证了该协议的有效性和正确性,仿真结果表明系统除了在有限时间内获得更快的收敛速度外,还具有良好的暂态性能.     

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.