李雅普诺夫

结果非线性动力学研究方法对糖尿病患者HRV分析的结果表现出很强的特异性，尤其是李雅普诺夫指数、近似熵和非线性能量算子。

Results The nonlinear indices of both DAN patients and patients without obvious DAN were significantly different from those of the normal subjects , especially in terms of Lyapunov exponent , approximate entropy , and nonlinear energy operator .

每一步把状态坐标变换、一个给定的李雅普诺夫函数和虚拟控制联系起来，最终得到一个控制李雅普诺夫函数（clf）。

In each step , the transformation of state coordinate , an known Lyapunov function and virtual control are connected and a control Lyapunov function is derived finally .

首先建立了一种基于李雅普诺夫变换的SINS等价误差模型。

An equivalent error model of SINS was established by Lyapunov transform .

冠心患者与健康人同步12导联ECG信号的李雅普诺夫指数谱比较研究

A comparative study of Lyapunov spectra of CAD patients ' and healthy people 's synchronous 12-lead ECG signals

本文主要介绍线性定常系统的时域稳定性分析、频域稳定性分析和李雅普诺夫稳定性分析时MATLAB函数的应用。

This article mainly introduce the applications of MATLAB - function in time - domain 、 s - domain and Lyapunov stability analysis of linear constant system .

利用李雅普诺夫稳定性分析方法，提出了一种自适应模糊控制方法能稳定一类不确定非线性MIMO纯反馈系统。

An adaptive fuzzy control approach is developed to stabilize a class of uncertain MIMO pure-feedback systems using Lyapunov stability analysis method .

依据李雅普诺夫稳定性理论和切换系统理论设计基于观测器的状态反馈控制律，获得利用Matlab工具箱求解的线性矩阵不等式条件。

Based on Lyapunov stability theory and switching system theory , observer-based state feedback control law is designed . The linear matrix inequality conditions are established by Matlab Toolbox .

基于控制李雅普诺夫函数的Sontag＿Type控制是仿射系统鲁棒镇定中的重要控制律。

The Sontag-Type control based on the control Lyapunov function ( CLF ) is an important control law in robust stabilization of affine systems .

对于跟随者的分布式控制策略采用个体的速率信息，然后，基于经典的李雅普诺夫（Lyapunov）理论，具体分析了闭环系统的稳定性。

The designed distributed coordination laws for the followers adopts the agents ' velocity information , then based on the classical Lyapunov theory , the stability of the closed-loop system is analyze in detail .

通过计算N台激光阵列的李雅普诺夫指数表明，当激光系统出现混沌同步时，系统的最大李雅普诺夫指数大于零，激光系统的参数范围完全处于混沌状态。

The calculation of the Lyapunov exponents in the array of N lasers shows that the laser system is in the chaotic states when the largest Lyapunov exponents are greater than zero . The parameters in the laser system are in the chaotic states .

基于分段连续的李雅普诺夫函数方法，给出了系统稳定且满足H∞范数界的充分条件和H∞状态反馈控制器的设计方法。

By using piecewise continuous Lyapunov function , a sufficient condition on robust stability with H_ ∞ norm bound is obtained . Moreover , a state feedback controller is developed to guarantee the closed-loop system being robustly stable with H_ ∞ norm bound .

应用脉冲控制的基本思想及李雅普诺夫（Lyapunov）函数方法对一类非线性动力系统的混沌控制，提出了采用指数稳定和非线性脉冲系统渐近稳定的一般准则来保证脉冲控制是全局渐近稳定的。

Applying the method of impulsive control and Lyapunov functions , some new general criteria exponential stability and asymptotical stability of nonlinear impulsive systems were established to ensure that the impulsive control is globally asymptotically stable .

KaplanYorke猜测认为吸引子的自然测度维数等于李雅普诺夫维数。

The Kaplan Yorke conjecture , which asserts that Lyapunov dimension equals to the dimension of the natural measure , is examined for spatiotemporal chaotic systems .

为寻求各种类型系统的镇定设计方法，从矩阵A的对称分支阵H（A）入手，利用李雅普诺夫稳定理论、LMI和矩阵理论，研究了一类局部稳定系统。

Through H ( A ), the symmetric part of matrix A , a class of stable part system is studied by employing Lyapunov stable theory , LMI and matrix theory . A sufficient condition for absolute part stable systems is given .

本文通过相关维检验、李雅普诺夫指数检验、BDS检验和返回临近（CR）检验对中国股票市场的混沌特征进行了分析，获得中国股票市场是混沌的有力证据。

We have tested the chaotic characteristics by using correlation dimension test , Lyapunov exponent test , BDS test and close return ( CR ) test . The conclusion indicates that Chinese stock market is chaotic .

考察这类系统的扰动情形，基于一定条件下的输入到状态稳定控制李雅普诺夫函数，给出了Sontag型输入到状态镇定设计。

Furthermore , based on an input-to-state stable CLF under appropriate conditions , a Sontag-type input-to-state stabilizer is designed for this kind of cascaded systems with perturbation .

用李雅普诺夫函数法与尝试法相结合的方法，构造了1组典型的非线性反馈函数，实现了2个超混沌Rossler系统的同步。

Using the Lyapunov function and method of trial and error , group of typical nonlinear feedback functions is constructed for synchronizing hyperchaos in two Rossler systems .

通过函数阵是PDD矩阵的李雅普诺夫函数和变量替换的方法，以线性矩阵不等式（LMI）的形式给出了系统渐近稳定的充分条件和输出反馈控制器设计方法。

By using Lyapunov function with PDD matrix and variable transformation , a sufficient condition on robust stability for this class of fuzzy systems is derived . Moreover , a robust control design approach is developed .

提出利用李雅普诺夫变换建立了一种易于进行分析的SINS动基座误差模型，同时论证了SINS与平台式惯导系统（GINS）模型的等价关系。

Using the Lyapunov transformation , an easy for the characteristic analysis of SINS error model was proposed on moving bases , and the equivalence of SINS and gimbaled inertial navigation system ( GINS ) error model was discussed .

理论上，借助李雅普诺夫函数及Nussbaum函数引理，证明了闭环系统的稳定性。

By means of Lyapunov function and Nussbaum function lemmas , it is proved theoretically that the designed adaptive nonlinear controller can guarantee the stability of close-loop control system .

同时利用李雅普诺夫稳定性原理，设计一种包含开关切换量的反馈控制器，实现不同状态下Cuk变换器同步控制。

At the same time , designs a plan of the feedback controller that encloses the switching variables to achieve synchronization control of Cuk converter under different states based on the Lyapunov stability theory .

根据李雅普诺夫稳定性理论，基于线性矩阵不等式（LMI），利用分散化并行分布补偿（PDC）的方法设计了基于观测器的控制器，给出了实现该非线性系统保性能控制的充分条件。

According to Lyapunov stability theory , the scheme of decentralized PDC ( Parallel Distributed Compensation ) fuzzy control was designed via LMI method , and apart from the above , the sufficient condition that ensures guaranteed cost control of nonlinear system was proposed .

通过构造适当的李雅普诺夫函数，推导出带d-q轴电流误差微分项的自适应律和带d-q轴电流误差积分项的控制律，并引入抗饱和积分器，提高系统的动态性能。

The adaptive law with the differential term and the control law with integral term of d-q axis current error are deduced by constructing the suitable Lyapunov function , and the anti-windup integrator is added to improve the dynamic performance .

文中考虑了暂态过程中磁链变化及AVR控制系统的作用，导出相应的微分方程组，并构成新的李雅普诺夫函数，用以评价电力系统运行的暂态稳定性。

Considering the change of magnetic linkage ( or electromotance ) and the effects of AVR control system , this paper defines the differential equations describing system with 2-axes excitation machines . It also forms a new Lyapunov function for evaluating transient stability of the power system .

指出控制李雅普诺夫函数（源于松弛控制）正是零状态可检测性的一种刻画，并由此区别两类镇定控制：无源性控制和Sontag型控制。

The notion of control Lyapunov functions ( CLF ) , originated from relaxed Controls , is newly understood as the characterization of zero-state detectability property , thus the difference between the Sontag-type control and the passivity-based controller is clarified accordingly .

目前所采用的方法主要有公共控制李雅普诺夫函数（CCLF）方法、多李雅普诺夫函数方法、驻留时间法等。

At present , the methods using Common Control Lyapunov Function method ( CCLF ), Multiple Lyapunov Function method and Dwell-time method , play an important role .

基于这一认识，也考虑到控制李雅普诺夫函数难于构造，我们抽象出弱控制李雅普诺夫函数概念，并证明了基于弱控制李雅普诺夫函数的Sontag-Type控制的镇定作用和优化特性；

Due to this recognition and the fact that control Lyapunov functions are difficult to be constructed , we propose the concept of weak control Lyapunov function and then prove the stabilizing property and the robustness of Sontag-Type control .

本文构造加权向量1-范数型李雅普诺夫函数。

Lyapunov 's function with weighted vector 1-norm form is constructed .

四元数体上李雅普诺夫矩阵方程解的特征确定法

Characteristic Determinative Method of Lyapunov Matrix Equation Solution on Quaternion Field

包括标量李雅普诺夫函数法和向量李雅普诺夫函数法。

Including the scalar Lyapunov approach and the vector Lyapunov approach .