关于伽玛函数和不完全伽玛函数单调性的注记

利用含有两参数拓广加权平均值的单调性和不等式,我们证明了三类比的伽玛函数在条件r＞0,s＞0和x＞0下是递增的,Γ(s),Γ(s,x)和γ(s,x)分别表示伽玛函数和不完全伽玛函数.据此关于伽玛函数和不完全伽玛函数的单调性结果和不等式被推广了,同时给出了伽玛函数一些结果的证明.     

K-解析函数的Hilbertert边值问题

定义和讨论了K-解析函数在典型域S~+={z:|z(k)|1}外的K-对称扩张函数,利用它把K-解析函数的Hilbert边值问题转化为Riemann边值问题,得到了K-解析函数类F(D(k))中Hilbert边值问题与Dirichlet边值问题的可解条件及其解的表达式.而解析函数和共轭解析函数都是K-解析函数的特例,所得结果,包含了解析函数和共轭解析函数中的相应结论.     

基于凸优函数的Newton类方法的收敛定理

本文研究了求解Banach空间上非线性算子方程f(x)=0的Newton类方法的收敛性.利用优函数原理,在A(x0)1f满足关于某一凸优函数的广义Lipschitz条件下,得到了Newton类方法的一个半局部收敛定理.同时,当f和A(x)及初始点x0给定时,针对广义Lipschitz条件构造了相应的优函数,推广了Newton类方法的相关结果.     

带变量核的奇异积分算子的加权不等式北大核心CSCD

利用核函数Ω(x,y)的性质,讨论了带变量核奇异积分算子T(f)的相关性质,并得到了当核函数Ω满足Dini型条件时该类算子的加权不等式,从而推广了以往非变量核的结果.     

凸函数的一个等价性质

函数的凸性在研究不等式、函数逼近论等领域有着十分重要的应用,但是在不同条件下的凸函数具有不同的一些等价性质.利用凸函数已有的性质及确界定理,给出并证明了凸(严格凸)函数的又一等价性质,所得结果与在可导条件下凸函数的不等式性质类似.     

一类完全重构滤波器的精度条件

本文研究了如何构造满足精度条件的小波滤波器.利用频域分析方法,给出了关于尺度函数精度条件的新结果以及满足精度条件的几个例子.     

一类带概率互补约束的随机优化问题的最优性条件

主要讨论了一类带概率互补约束的随机优化问题的最优性条件.首先利用一类非线性互补(NCP)函数将概率互补约束转化成为一个通常的概率约束.然后,利用概率约束的相关理论结果,将其等价地转化成一个带不等式约束的优化问题.最后给出了这类问题的弱驻点和最优解的最优性条件.     

K-解析函数的Riemann边值问题

引入了(分片)K-解析函数和Cauchy型K-积分的概念.利用K-对称变换的方法研究了Cauchy型K-积分的某些性质,然后借助函数在曲线上的指标与这些Cauchy型K-积分的性质,得到了K-解析函数类中的Riemann边值问题的可解条件和解的表达式以及它们与指标之间的关系.而解析函数和共轭解析函数都是K-解析函数的特例,文中所得结果,推广了解析函数和共轭解析函数中的相应结论.     

非凸多目标优化中真有效解的一个非线性标量化性质

基于Pascoletti-Serafini标量化方法,利用罚函数思想提出了一类新的标量化函数,进而获得非凸多目标优化问题真有效解的充分条件和必要条件.该结果的建立不需要目标函数的像集有界这一条件,故文章是对Akbari等人[J.Optim.Theory Appl.,2018,178(2):560-590]建立的相应标量化结果的改进.     

一类非线性多目标分式规划的最优性条件和对偶

本文利用亚线性函数和广义(F,α,ρ,d)-凸性的概念,给出了一类非线性多目标分式规划的充分性条件和对偶结果.     

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.     

一类具混合时滞随机神经网络稳定性的推广与应用

将一类具有混合时滞随机神经网络均方渐近稳定的判据推广到不确定神经网络的鲁棒稳定性,所导出的判据都表示为线性矩阵不等式(LMI)的形式,可通过使用一些标准的数值方法求解.最后给出了一个简单的例子说明所提出的判定条件的有效性和可应用性.     

LMI优化的一种原对偶中心路径算法

系统和控制理论中许多重要的问题,都可转化为具有线性目标函数、线性矩阵不等式约束的LMI优化问题,从而使其在数值上易于求解.本文给出一种求解LMI优化问题的原对偶中心路径算法,该算法利用牛顿方法求解中心路径方程得到牛顿系统,并将该牛顿系统对称化以避免得到非对称化的搜索方向.文章详细分析了算法的计算复杂性.     

时变时滞BAM神经网络系统的指数稳定性分析

利用Lyapunov稳定性理论和线性矩阵不等式技术,得到了保证时变时滞BAM神经网络系统指数稳定性的时滞依赖稳定性准则.所给的准则可用Matlab中的LMI控制工具箱进行验证.仿真实例进一步说明了结果的有效性.     

Global asymptotic stability of stochastic reaction-diffusion neural networks with time delays in the leakage terms

In this paper, a class of stochastic reaction-diffusion neural networks with time delays in the leakage terms is investigated. By using the Lyapunov functional method and linear matrix inequality (LMI) approach, sufficient conditions are derived to ensure the global asymptotic stability of an equilibrium point of the networks in the mean square. The results can be easily solved by MATLAB LMI toolbox. Finally, a numerical example is given to demonstrate the effectiveness and conservativeness of our theoretical results.     

The projective method for solving linear matrix inequalities

Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.     

A delay-range-dependent uniformly asymptotic stability criterion for a class of nonlinear singular systems

This paper investigates a class of nonlinear singular systems. Based on the Lyapunov functional method and the free-weighting matrix method, a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Two examples are given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of nonlinear singular systems.     

An LMI approach to decentralized guaranteed cost control for a class of uncertain nonlinear large-scale delay systems

The guaranteed cost control problem via the decentralized robust control for nonlinear uncertain large-scale systems that have delay in both state and control input is considered. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequality (LMI). It is shown that the decentralized local state feedback controllers can be obtained by solving the LMI.     

Global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays: An LMI approach

In this paper, we consider the stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. By utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, some sufficient LMI-based conditions are obtained to guarantee the global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. These conditions can be easily checked via the MATLAB LMI toolbox. Moreover, the obtained results extend and improve the earlier publications. Finally, a numerical example is provided to demonstrate the low conservatism and effectiveness of the proposed LMI conditions.     

Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Systems Using Linear Matrix Inequalities

This paper considers the output feedback guaranteed cost controller design problem for uncertain discrete-time systems. The uncertainty is assumed to be of linear fractional form, unstructured, and is allowed to be time-varying. It is proved that the existence of a guaranteed cost controller is equivalent to the feasibility of a certain linear matrix inequality (LMI), and that a full-order output feedback controller can be constructed in terms of the feasible solution to the LMI. Furthermore, a convex optimization problem is introduced for the selection of a suitable controller minimizing a specified cost bound.