具有有界控制输入的状态反馈控制系统闭环稳定性

本文基于李雅普诺夫定理,给出了具有有界控制输入的离散时间系统和连续时间控制系统的闭环渐近稳定性判据。利用不考虑控制约束时闭环系统李雅普诺夫矩阵方程解,得出了当控制输入有界时,线性状态反馈控制系统为渐近稳定的充分条件。这些判据具有简单的形式,并且易于计算。     

噪声环境中时延区间CNN网络鲁棒稳定性

由于采用大规模集成电路方法实现细胞神经网络(cellular neural networks,CNN),其 电路所产生的噪声不可避免,实际的网络都是在噪声环境中进行工作的,弄清楚这些随机干扰 是如何影响网络的稳定性,在网络设计时非常关键.利用鞅收敛定理、李雅普诺夫直接法和矩阵 分析的方法,研究了白噪声干扰下时延区间细胞神经网络承受扰动的能力,得到了仅依赖系统 参数的充分性代数判据.所得结果在系统设计时检验较为方便.     

滞后型控制系统的稳定性判据

本文根据李雅普诺夫稳定性理论,推导出滞后型控制系统x(t)=Ax(t)+Atx(t-T) 无条件稳定的充分条件.并且证明所建立的稳定性代数判据,不仅简明易用,且能获得较大的 稳定区域.     

高精度伺服系统低速问题研究

采用相平面法、代数分析法和李雅普诺夫稳定性定理得出了三阶系统克服低速滞滑爬 行的判定定理.通过该判定定理得到系统参数与低速滞滑爬行的关系,在满足常规稳定控制器 参数选择范围的基础上,给出了为消除低速滞滑爬行,PID控制器参数还应满足的条件.该判定 定理简单实用,对于高精度伺服系统的调试具有很好的指导意义.     

智能电动车EPS鲁棒性控制律的建模与仿真

智能电动汽车配备电动助力转向系统(EPS)以提高转向系统的稳定.EPS是非线性系统,为了改进其鲁棒性能,结合EPS的结构和动力学特性,建立了EPS的动力学方程.构建结合整车、轮胎、EPS系统的整体仿真模型,利用李雅普诺夫方法的克拉索夫斯基定理设计EPS控制律,并用李雅普诺夫再设计方法设计具有鲁棒性的EPS控制律.在多领域建模软件Dymola中对智能电动汽车转向系统建模,并进行阶跃仿真,结果表明,李雅普诺夫再设计方法得到的EPS控制律具有较强鲁棒性.     

一种绳牵引并联机器人系统控制律设计及Lyapunov 稳定性分析

根据绳牵引并联机器人系统的耦合性和非线性,以6-DOF八绳牵引并联机器人(WDPR-8)系统为研究对象,设计一种基于系统动力学方程的PD控制律,并构造出一种李雅普诺夫函数;基于李雅普诺夫稳定性理论以及LaSalle定理对非线性并联控制系统进行稳定性分析,结果表明,WDPR-8支撑系统呈渐近稳定特性.针对用于风洞试验的飞机模型支撑,通过仿真实验验证所设计控制律的正确性和可行性.仿真结果表明,系统的控制性能良好,可为实际应用提供依据.     

20世纪运动稳定性研究的三个重要结果

本文论述20世纪运动稳定性理论研究的三个重 要结果：李雅普诺夫函数、谢聂稳定判据、卡利托洛夫定理.这三个结果都是对一般的连续 系统作出的,结论明确,简单实用,因而具有广泛的应用性．     

一种继电自动调节系统平衡位置的全局稳定性

本文对切除硬反馈的继电自动调节系统平衡位置的全局稳定性进行了初步的讨论.利用A.M.李雅普诺夫的直接法和B.A.雅库波维奇的结果,给出系统平衡位置全局稳定性的若干频率式的充分判据.文末应用同样的方法,讨论了继电直接调节系统平衡位置的全局稳定性,得到了一个较文献[2,3]易于应用的频率式的充分判据.     

具有非线性滞后关联的随机大系统的分散镇定

本文通过利用李雅普诺夫函数和李雅普诺夫矩阵方程的性质，对具有非线性滞后关联的一类随机大系统建立了分散鲁棒镇定的判据，所得闭环随机大系统的和稳定性不依赖于任意实数滞后，并对不确定系数矩阵和随机扰动强度具有鲁棒性。     

一种继电自动調节系統平衡位置的全局稳定性

本文对切除硬反馈的继电自动调节系统平衡位置的全局稳定性进行了初步的讨论.利用A.M.李雅普诺夫的直接法和B.A.雅库波维奇[1]的结果,给出系统平衡位置全局稳定性的若干频率式的充分判据.文末应用同样的方法,讨论了继电直接调节系统平衡位置的全局稳定性,得到了一个较文献[2,3]易于应用的频率式的充分判据.     

离散混沌系统的线性和非线性反馈同步法及其条件

基于离散系统稳定性理论和Pecora-Carroll混沌同步定理，研究了多变量离散混沌系统的同步问题．提出了线性和非线性反馈同步控制方法，同步系统反馈控制器由线性和非线性两部分组成，响应系统受驱动系统的所有变量驱动．通过分析误差系统的特征方程和计算响应系统的最大条件Lyapunov指数，分别导出了离散混沌系统的同步条件．将该方法应用于Henon映射系统，实现了两Henon混沌系统的同步控制．讨论了混沌系统的同步性能与控制参数的关系．基于Matlab软件的数值仿真结果表明了该方法的有效性．     

Stability analysis of continuous-time periodic systems via theharmonic analysis

Asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems is studied by harmonic analysis. It is first shown that stability can be examined with what we call the harmonic Lyapunov equation. Another necessary and sufficient stability criterion is developed via this generalized Lyapunov equation, which reduces the stability test into that of an approximate FDLCP model whose transition matrix can be determined explicitly. By extending the Gerschgorin theorem to linear operators on the linear space l₂, yet another disc-group criterion is derived, which is only sufficient. Stability of the lossy Mathieu equation is analyzed as a numerical example to illustrate the results     

自治混沌系统普适广义投影同步理论及应用

针对自治混沌系统，基于系统稳定性理论，通过设计合适的非线性反馈控制器，给出了普适的广义投影同步定理．定理中函数的选择可以为系统的线性或非线性函数，更具灵活性和普适性；文中理论还可以通过调整参数提高广义投影同步的速度．数值仿真进一步验证了本文理论的有效性和实用性．     

混沌Ikeda系统同步及其在保密通信中的应用

针对一类时滞Ikeda混沌系统,利用Lyapunov稳定和微分不等式,研究了其指数同步问题。基于线性矩阵不等式理论得到了指数同步的充分条件,给出了指数同步控制器的设计方法,利用混沌掩盖将该同步方法应用于保密通信。仿真表明,该方案具有同步速度快、鲁棒性良好等优良性能。     

Delay-independent stability criteria for linear continuous systems with time-varying delays

New stability criteria for linear continuous systems with multiple time-varying delays are established by the Lyapunov function approach based on a new stability theorem for general type of retarded dynamical systems. A new technique for estimating the derivative of Lyapunov function along the solution of system at some specific instants is used so that the case of multiple time-varying delays can be dealt with less conservatively. In addition, (i) every criterion has only one tuning parameter matrix P>0 as the Lyapunov-type stability criterion for the corresponding linear continuous system without delays does; (ii) all the criteria are given in LMI forms and hence they are numerically tractable. It is remarked that the established criteria are less conservative than the existing ones in the literature. Three examples are given to illustrate the proposed method and to show the superiority of the obtained results to the existing ones in the literature.     

Anti‐Synchronization and Intermittent Anti‐Synchronization of Two Identical Delay Hyperchaotic Chua Systems Via Linear Control

This work is concerned with anti‐synchronization and intermittent anti‐synchronization of two identical delay hyperchaotic Chua systems with linear control approaches. In the first two schemes, based on Lyapunov stability theory, some sufficient conditions for achieving anti‐synchronization of two identical delay hyperchaotic Chua systems are derived, numerical simulation results are presented to demonstrate the effectiveness of the proposed anti‐synchronization schemes. In the third scheme, the anti‐synchronization conditions are obtained by numerical method. In the fourth scheme, only one state of the response system is controlled via linear control, we report an interesting phenomenon of intermittent anti‐synchronization.     

时变时滞Lurie控制系统的绝对稳定性

基于Lyapunov稳定性定理,利用线性矩阵不等式方法给出了系统绝对稳定的判别准则.讨论了具有多个时变时滞的Lurie直接控制系统和Lurie间接控制系统的绝对稳定性.所得结论是时滞无关的,即绝对稳定性充分条件仅依赖于时滞导数的大小,特别地,时滞可为无界函数.通过一个示例说明有时得到时滞相关的绝对稳定性条件比时滞无关的稳定性条件具有更大的保守性,促使今后寻找另外的方法和工具得到保守性较低的稳定性条件.仿真示例同时说明此方法对时滞为无界函数时的有效性.     

Exponential synchronization of nonlinear multi‐agent systems with time delays and impulsive disturbances

The problem of cooperative synchronization of nonlinear multi‐agent systems with time delays is investigated in this paper. Compared with the existing works about synchronization (or consensus) of multi‐agent systems, the method in this paper provides a more general framework by considering nonlinear multi‐agent systems with time delays and impulsive disturbances. The model in this paper is sufficiently general to include a class of delayed chaotic systems. Based on the Lyapunov stability theory and algebraic graph theory, sufficient conditions are presented to guarantee the cooperative exponential synchronization for these multi‐agent delayed nonlinear systems. These conditions are expressed in terms of linear matrix inequalities, which can easily be checked by existing software tools. It is seen that the Lyapunov functions must be constructed based on the graph topology to prove synchronization. The well‐known master–slave (drive‐response) synchronization of two chaotic delayed systems is a special case of this paper, and therefore, the results in this paper are also useful for practical applications in secure communication. Simulation results verify the effectiveness of the proposed synchronization control algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Sufficient Conditions for Stability of Periodic Linear Impulsive Delay Systems

For a linear periodic system with impulsive action and delay, new approaches to the study of stability were proposed on the basis of the methods of spectral theory of linear operators, direct Lyapunov method, and N.G. Chetaev method for construction of the Lyapunov functions for the periodic linear systems, as well as the perturbation method for construction of the Lyapunov functions. These methods underlie the sufficient conditions for asymptotic stability of the linear periodic systems with impulsive action and delay. We gave some illustrative examples of studying stability of such systems under different assumptions about the dynamic properties of the continuous and discrete components of the impulsive system.     

时滞混沌系统的同步与反同步及其在保密通信中的应用

根据Lyapunov稳定性理论结合线性矩阵不等式技巧,研究了一类时滞混沌神经网络的同步与反同步问题,设计了各自的状态反馈控制器,并从理论上实现了此类时滞混沌系统的同步与反同步。最后将此类混沌系统应用于保密通信,通过同步与反同步系统的切换,设计出具体的数字保密通信方案,数值仿真验证了该方法的有效性。