1) Lyapunov-Krasovskii functional
Lyapunov-Krasovskii函数
1.
When the activation function satisfies the condition of Lipschitz continuity,two sufficient conditions are established for the globally robust stability of the equilibrium point by suitably choosing Lyapunov-Krasovskii functional.
通过选取合适的Lyapunov-Krasovskii函数,建立了两个全局鲁棒稳定判据。
2.
Based on a RBF neural network online approximation model, a state feedback adaptive controller is obtained by constructing a novel Lyapunov-Krasovskii functional.
在RBF神经网络在线估计模型的基础上,本文通过设计新的Lyapunov-Krasovskii函数推导出了新的状态自适应控制器。
2) fuzzy Lyapunov-Krasovskii function
模糊Lyapunov-Krasovskii函数
1.
The H∞ control problem of discrete T-S fuzzy systems with time-delay are studied via fuzzy Lyapunov-Krasovskii function.
研究了离散时滞T-S模糊系统基于模糊Lyapunov-Krasovskii函数的H∞控制问题。
2.
The stability analysis and controller design problem of discrete T-S fuzzy model with delay are studied via fuzzy Lyapunov-Krasovskii function.
研究了离散时滞T-S模糊模型基于模糊Lyapunov-Krasovskii函数的稳定性分析及控制器设计问题。
3.
Based on the fuzzy Lyapunov-Krasovskii function(LFK),a fuzzy controller is designed to acquire globally asymptotical stability for the discrete uncertain fuzzy time-delay system with the method of parallel distributed compensation(PDC).
基于模糊Lyapunov-Krasovskii函数,应用并行分布补偿算法,设计了使模糊系统全局渐近稳定的控制器,提出并证明了一个新的判别闭环不确定离散时滞模糊系统鲁棒H∞渐近稳定的充分条件。
3) Lyapunov-Krasovskii functional
Lyapunov-Krasovskii泛函
1.
By adopting Lyapunov-Krasovskii functional and dissi-pative theory,sufficient conditions are given to ensure the existence of a memoryless state feedback control law,which guarantees the stability of the closed-loop system.
采用Lyapunov-Krasovskii泛函和耗散性理论,给出了保证闭环系统渐近稳定的无记忆状态反馈控制律存在的充分条件,该条件同时保证闭环系统满足γ-次优H∞性能,为控制器的设计提供了理论依据。
2.
Applying a stabilizing state feedback control to systemsm,aking use of the Lyapunov-Krasovskii functional and combining the method of the linear matrix inequalities(LMI)t,he sufficient conditions of robust BIBO stabilization for T-S fuzzy control systems are obtained.
研究了一类具有不确定系数的T-S模糊控制系统的鲁棒BIBO镇定问题,应用稳定的状态反馈控制,通过构造Lyapunov-Krasovskii泛函,采用线性矩阵不等式(LMI)方法,给出了T-S模糊连续控制系统Robust有界输入有界输出镇定的充分条件;当参考的输入信号r(t)≡0时,给出了T-S模糊连续控制系统的零解鲁棒镇定的充分条件。
3.
Constructing a suitable Lyapunov-Krasovskii functional and based on the scheme of decentralized control,the design of a control law is proposed to ensure the global asymptotic synchronization of state trajectories of two chaotic neural networks of which the structure are the same and the initial conditions are different.
基于分散控制策略,通过构造适当的Lyapunov-Krasovskii泛函,给出了保证两个具有相同结构但初始条件不相同的时滞混沌神经网络全局渐近同步的控制律设计方法。
4) Lyapunov-Krosovskii functional
Lyapunov-Krasovskii型泛函
1.
By using of the LMI and Lyapunov-Krosovskii functional,a memoryless adaptive state feedback controller is proposed,which can guarantee the closed-loop system is globally stable in the sense of uniform ultimate boundedness.
结合线性矩阵不等式和Lyapunov-Krasovskii型泛函设计出了一种无记忆自适应状态反馈控制器,并证明此控制器使得闭环系统最终一致有界;仿真例子说明了结论的有效性。
2.
By using the Lyapunov stability theory and Lyapunov-Krosovskii functional,we propose a robust adaptive state feedback controller,which can guarantee that the closed-loop system is globally stable in the sense of uniform ultimate boundedness,and the st.
基于Lyapunov稳定性理论和Lyapunov-Krasovskii型泛函,设计了一种鲁棒自适应状态反馈控制器,并证明了此控制器使得闭环系统一致最终有界,且系统的状态将一致渐近趋于0。
5) augmented Lyapunov-Krasovskii functional
增广Lyapunov-Krasovskii泛函
1.
Being different from existing reports,the novel delay-dependent robust stability criteria for interval recurrent neural networks with mixed time-varying delays employ a new augmented Lyapunov-Krasovskii functional.
与之前的处理方法不同,在本文中通过使用一种新型的增广Lyapunov-Krasovskii泛函,从而得到了一类新颖的关于区间递归神经网络的时滞依赖全局鲁棒稳定性判据。
6) fuzzy Lyapunov-Krasovskii functional
模糊Lyapunov-Krasovskii泛函
1.
Based on a fuzzy Lyapunov-Krasovskii functional(LKF) and fuzzy free-weighting matrices with time-delay,a new delay-dependent robust stability criterion is proposed and proved for the close-loop fuzzy system.
基于模糊Lyapunov-Krasovskii泛函(LKF),引入多个模糊时滞自由权值矩阵,提出并证明了闭环系统新的时滞相关鲁棒H∞渐近稳定的充分条件。
补充资料：高斯函数模拟斯莱特函数
尽管斯莱特函数作为基函数在原子和分子的自洽场（SCF）计算中表现良好，但在较大分子的SCF计算中，多中心双电子积分计算极为复杂和耗时。使用高斯函数(GTO)则可使计算大大简化,但高斯函数远不如斯莱特函数(STO)更接近原子轨道的真实图象。为了兼具两者之优点，避两者之短,考虑到高斯函数是完备函数集合,可将STO向GTO展开：
式中X(ζS,A,nS,l,m)定义为在核A上，轨道指数为ζS，量子数为nS、l、m 的STO；g是GTO：
其变量与STO有相似的定义；Ngi是归一化常数：
rA是空间点相对于核A的距离;ci是组合系数；K是用以模拟STO的GTO个数（理论上，K→∞，但实践证明K只要取几个，便有很好的精确度）。
ci和ζ在固定K值下, 通过对原子或分子的 SCF能量计算加以优化。先优化出 ζS＝1 时固定K值的ci和(i＝1,2,...,K)，然后利用标度关系式便可得出ζS的STO展开式中每一个GTO的轨道指数，而且，ci不依赖于ζS,因而ζS＝1时的展开系数就是具有任意ζS的STO的展开系数。对不同展开长度下的展开系数和 GTO轨道指数已有表可查。
式中X(ζS,A,nS,l,m)定义为在核A上，轨道指数为ζS，量子数为nS、l、m 的STO；g是GTO：
其变量与STO有相似的定义；Ngi是归一化常数：
rA是空间点相对于核A的距离;ci是组合系数；K是用以模拟STO的GTO个数（理论上，K→∞，但实践证明K只要取几个，便有很好的精确度）。
ci和ζ在固定K值下, 通过对原子或分子的 SCF能量计算加以优化。先优化出 ζS＝1 时固定K值的ci和(i＝1,2,...,K)，然后利用标度关系式便可得出ζS的STO展开式中每一个GTO的轨道指数，而且，ci不依赖于ζS,因而ζS＝1时的展开系数就是具有任意ζS的STO的展开系数。对不同展开长度下的展开系数和 GTO轨道指数已有表可查。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条