正定函数

我们主要是利用找到一个公共Lyapunov函数使得整个系统满足一定的条件，则系统就是稳定的，文中还分析了二次稳定性，对于二次稳定性选用二次正定函数，它相似于公共Lyapunov函数。

We find a common Lyapunov function to make the whole system satisfy some conditions , so the system is stable . We also base on the quadratic stability , to the quadratic stability , choose a quadratic positive-definite function which is similar to the common Lyapunov function .

消耗率系数为常数的Lanchester型战争方程的终止问题在[1]、[2]中得到解决，本文利用正定函数可得到变系数Lanchester型现代战争方程的转折点或终止问题。

Termination problem about Lanchester equation which consumption coefficients are constant has been solved . Appling positive definite function , this paper obtained the turning point and termination problem about Lanchester equation with variable coefficients .

幺模群上的不可分解正定函数及其应用

Irreducible positive definite function on unimodular group and Its Applications

一类新的正定函数

A class of new positive definite functions

经典的李雅普诺夫稳定性定理提供了定号到定号模式的稳定性分析方法，即：选择一个正定函数V>0，确定负定的V<0沿系统的解成立。

The classical Lyapunov stability theorems work in the so called sign-definite-to-sign-definite mode , i.e. from a sign positive definite function V > 0 to a sign negative definite derivative V < 0 of the function along the solution of system .

通过构造一个含有待定矩阵变量的正定Lyapunov函数，推导具有LMI形式的时延相关的稳定性条件。

By constructing a positive definite Lyapunov function with undecided matrix variables , the delay-related stability condition in LMI form has been deduced .

但是，在某些特定的领域中，所使用的核函数不能确保为半正定核函数，如神经网络中的Sigmoid核。

However , in some certain specific areas , kernel function can not be guaranteed as positive definite kernel function , such as Sigmoid kernel function in neural networks .

本文主要研究以下二个部分的内容：1.分析掌纹和指纹自身的特点，研究现有的各种核函数所存在的问题，提出了条件正定核函数（CPD）。

Palmprint and fingerprint analysis of the characteristics of their own to study the various existing problems in the nuclear function of the proposed terms of positive definite kernel ( CPD ) .

设计了分段仿射控制器（PWA），在PWA近似模型期望闭环平衡点附近区域设计一个局部线性控制器，应用分段正定李雅普诺夫函数证明闭环系统在整个非线性域内稳定。

A PWA controller is designed . A local linear controller is determined for the PWA approximate model in the region where the desired close-loop equilibrium point lies . Stability of the close-loop system in the whole domain of the nonlinearity is proved using a piecewise quadratic Lyapunov function principle .

给出了正交双线性函数基与正定双线性函数基；证明了：（1）每个双线性函数均可由正交双线性函数基惟一线性表出；

In this paper , We give concepts of orthogonal double linear function basis and positive definite double linear function basis , and show that ( 1 ) every double linear function can be lineally expressed by orthogonal double linear function basis ;

提出了构造尺度矩阵的一个简式公式，其对应的简式变尺度算法与正割法等价，当目标函数为正定二次函数时简式变尺度算法与BFGS方法等价。

A simple formula of forming metric matrices is put forward . The simple variable matric algorithm produced from the formula is equivalent to the secant method and when the aim function is positive definite quadratic function , it is equivalent to BFGS .

拟正定算子值函数与拟完全单调算子值函数

Quasi-positive definite operator functions and quasi-completely monotonic operator functions

用坐标变换求解正定二次函数最优值

The Coordinate Transformation Method to Determine the Optimal Vaule of Positive Definite Quadratic Function

圆弧搜索修正法求解正定二次函数的校正公式

A Correction Formula with Circular Arc Search for Unconstrained Minimization of Positive Definite Quadratic Function

用矩阵的正定性判定多元函数极值的存在性

Determination on the Existence of Extremum in Multivariable Functions by the Positive Definiteness of Their Matrices