李亚普诺夫函数

这种方法通过构造合适的前馈控制器，结合常规的模型参考自适应控制方法，选取适当的李亚普诺夫函数，运用李亚普诺夫稳定性定理证明了系统的渐进稳定性，得到自适应律，使系统控制器具有自适应性。

Based on the model reference adaptive control ( MRAC ) method , by constructing proper feedforward controller and Lyapunov function , and applying Lyapunov stability theorem in proving system asymptotically stability to get adaptive control law , the method constructs an adaptive control system .

利用模糊系统的逼近能力，后推设计方法及积分型李亚普诺夫函数，依次确定各虚拟控制及模糊系统中的可调参数的自适应律，并最终确定出控制律。

By utilizing the approximation capability of fuzzy systems , backstepping technique and integral - type Lyapunov function , each virtual control and the adaptation law of the adjustable parameters in the fuzzy systems are determined in turn . In the end , the control law is determined .

假设系统存在能量有界的外部扰动输入，通过构造合适的李亚普诺夫函数，得到了使得闭环控制系统有限时间有界并满足给定H∞性能指标的充分条件。

By constructing a proper Lyapunov function , a sufficient condition is given so that the closed-loop control system is finite-time bounded and satisfy the given H ∞ control index .

基于一种修改的李亚普诺夫函数的自适应模糊滑模控制

Adaptive fuzzy sliding mode control based on a modified Lyapunov function

并通过在李亚普诺夫函数中引入交叉项证明了控制律的全局稳定性；

Then the global stability of the control law was also achieved by adding of cross terms in Lyapunov candidate function .

选择一正定的李亚普诺夫函数，基于李亚普诺夫直接法求出混沌同步的控制量。

The Control for chaotic synchronization is directly designed based on lyapunov 's direct method by choosing a positive definite lyapunov function .

采用多李亚普诺夫函数方法设计控制器的切换律，系统在此切换律下可以达到渐近稳定。

Multiple Lyapunov functions method is introduced to design the switching law between controllers , the system is asymptotically stable under the switching law .

通过构造特殊的李亚普诺夫函数，分别考虑了时滞相关和时滞无关两种情形，得到了系统鲁棒绝对稳定的充分条件。

Via the constructive Lyapunuov function , the case independent of delay and dependent of delay is investigated respectively , and the sufficient conditions of robust absolute stability are gained .

利用多李亚普诺夫函数方法和平均驻留时间方法，设计状态反馈控制器，当执行器失效在允许的范围内保证系统依然有限时间稳定。

By using multiple Lyapunov functions and average dwell-time method , the state feedback controller is designed to guarantee the finite-time stability of switched systems with possible actuator failures in the permissible range .

提出了非保守力学系统的李亚普诺夫函数构造途径：定性分析的能量函数方法和可用于定量分析的系统分解方法，并给出了分别使用上述方法的充分性条件。

The author give ways to construct Liapunov function of a lagrange system with energy consumption : One gives qualitative analysis of the mechanical system , the other gives quantitative estimation as well as qualitative analysis of the asymptotic stability of the studied mechanical system .

从电力系统暂态能量函数出发，应用哈密顿系统理论首次提出新的李亚普诺夫函数。用该函数分析了具有切机切负荷稳定控制的简单电力系统的暂态稳定性。

Starting from the transient energy function of power system and by using the theory of Hamiltonian system , a new Lyapunov function is firstly constructed to analyze the transient stability of a simple power system with emergency control of generator tripping or load shedding .

根据李亚普诺夫稳定函数建立了时延神经网络渐近稳定性判据的充分条件。

In this paper , A sufficient condition for the asymptotic stability of the equilibrium point for the class of delayed neural networks is established according to Lyapunov function .

传统的暂态能量函数直接法虽然能提供稳定裕度，临界切除时间等信息，但由于在电力系统中无法找到严格的李亚普诺夫能量函数，所以其准确性得不到保障。

Though , the direct transient stability methods based on transient energy functions ( TEF ) can provide quantitative measures of stability such as stability margin and critical clear time , the poor precision caused by the approximation of transient energy functions is fatal .