论一阶模糊差分方程x_(n+1)=Ax_n+B

讨论一阶模糊差分方程xn+1=Axn+B(n=0,1,…)正解的存在性、有界性及正解的渐近表现.其中(xn)是正模糊数数列, A,B,x0是正模糊数.     

Block Diagonalization of Linear Difference Equations

A linear autonomous system of difference equations x k +1 = Ax k can be transformed to its Jordan normal form, i.e. , the transformed system is in block diagonal form and the blocks correspond to different eigenvalues. We generalize this result to arbitrary nonautonomous linear systems x k +1 = A k x k with invertible matrices A k ] Â N 2 N , k ] { … , m 1, 0,1, … }.     

On the Periodic Character of Some Difference Equations

We consider positive solutions of the following difference equation x n =max A x n m k , B x n m m , n =0,1,…, where A , B are any positive real numbers and k , m are any positive integers. We prove that every positive solution is eventually periodic and determine the period in terms of the parameters A , B , k , and m .     

Galois Theory of Difference Equations with Periodic Parameters

We develop a Galois theory for systems of linear difference equations with periodic parameters, for which we also introduce linear difference algebraic groups. We apply this to constructively test if solutions of linear q-difference equations, with q ∈ ?* and q not a root of unity, satisfy any polynomial ζ-difference equations with ζ ^t  = 1, t ≥ 1.     

论模糊差分方程xn+1=a+bxn/A+xn-1

讨论非线性模糊差分方程x_n+1=a+bx_n/A+x_n-1（n=0,1,…）正解的存在性、有界性及正解的渐近表现。其中是正模糊数数列、及初始值是正模糊数。     

Asymptotic Behavior of a Class of Nonlinear Delay Difference Equations

In this paper, we shall study the asymptotic behavior of solutions of difference equations of the form x n +1 = x n p f ( x n m k 1 , x n m k 2 ,…, x n m k r ), n =0,1,…, where p is a positive constant and k 1 ,…, k r are (fixed) nonnegative integers. In particular, permanence and global attractivity will be discussed.     

On Invariance Factors and Invariance Vectors for Difference Equations

In this paper, the concept of invariance factors and invariance vectors to obtain invariants (or first integrals) for difference equations will be presented. It will be shown that all invariance factors and invariance vectors have to satisfy a functional equation. This concept turns out to be analogous to the concept of integrating factors and integrating vectors for ordinary differential equations.     

输入采用标准模糊分划的模糊控制系统性质及稳定性分析

具体定义模糊控制系统输入变量的标准模糊分划，研究和证明输入采用标准模糊分划的模糊控制系统的有关性质。在此基础上，采用Lyapunov直接法研究该类模糊控制系统的稳定性，提出一个判定模糊控制系统稳定性的充分条件。该条件将以往方法要在所有的子系统中寻找一个公共的正定矩阵满足Lyapunov不等式，放宽为在各最大交叠规则组内分别寻找公共的正定矩阵，从而减小稳定性判定的保守性和难度。     

基于∨-·运算的Fuzzy矩阵方程的摄动问题

定义基于∨ - .运算的 Fuzzy矩阵 A的同解简化矩阵 ,利用 A的同解简化矩阵 A(1) 给出基于∨ - .运算的 Fuzzy矩阵方程的矩阵解法 ,并研究这类 Fuzzy矩阵方程的摄动问题。     

Difference Equations and Lettenmeyer's Theorem

Many classical results for ordinary differential equations have counterparts in the theory of difference equations, although, in general, the technical details for the difference versions are more involved than the corresponding ones for differential equations. This note surveys material related to a difference analogue of Lettenmeyer's theorem. The projection method of Harris et al. , developed to treat certain questions in the analytic theory of ordinary differential equations is used to obtain counterparts for linear difference equations as well as extensions to certain nonlinear differential and difference equations.     

Asymptotic Behavior of Solutions of Some Linear Difference Equations with Oscillatory Decreasing Coefficients

We investigate the asymptotic behavior of solutions of the system x ( n +1)=[ A + B ( n ) V ( n )+ R ( n )] x ( n ), n S n 0 , where A is an invertible m 2 m matrix with real eigenvalues, B ( n )= ~ j =1 r B j e i u j n , u j are real and u j p ~ (1+2 M ) for any M ] Z , B j are constant m 2 m matrices, the matrix V ( n ) satisfies V ( n ) M 0 as n M X , ~ n =0 X Á V ( n +1) m V ( n ) Á < X , ~ n =0 X Á V ( n ) Á 2 < X , and ~ n =0 X Á R ( n ) Á < X . If AV ( n )= V ( n ) A , then we show that the original system is asymptotically equivalent to a system x ( n +1)=[ A + B 0 V ( n )+ R 1 ( n )] x ( n ), where B 0 is a constant matrix and ~ n =0 X Á R 1 ( n ) Á < X . From this, it is possible to deduce the asymptotic behavior of solutions as n M X . We illustrate our method by investigating the asymptotic behavior of solutions of x 1 ( n +2) m 2(cos f 1 ) x 1 ( n +1)+ x 1 ( n )+ a sin n f n g x 2 ( n )=0 x 2 ( n +2) m 2(cos f 2 ) x 2 ( n +1)+ x 2 ( n )+ b sin n f n g x 1 ( n )=0 , where 0< f 1 , f 2 < ~ , 1/2< g h 1, f 1 p f 2 , and 0< f <2 ~ .     

模糊Logistic方程的稳定性

研究了具有广义Hukuhara导数的模糊Logistic方程,将模糊Logistic方程转化成两个常微分方程,分析了模糊Logistic方程平衡点的稳定性.结论表明,模糊Logistic方程平衡点的稳定性不同于确定的Logistic方程,丰富了模糊微分方程研究的内容.     

模糊一次方程求解的实际研究

传统的加法,减法,乘法和除法运算都属于自然运算,因此不能用于区间数（interval）的分析中,故需要进一步研究区间数的特殊的运算规律。本文介绍模糊集合理论中的区间数进行加、减、乘、除等特殊的算术运算规律为基础,主要介绍并提出模糊一次方程bx＋a=c的求解过程及方法,并给出其模糊方程的解。     

Global Behaviour of Solutions of Nonlinear Delay Difference Equations*

In this paper global asymptotic stability and asymptotic behaviour of solutions of nonlinear delay difference equations has been studied and a few sets of sufficient conditions for global asymptotic stability are derived.     

模糊随机微分方程解的存在唯一性

将实数空间上的随机微分方程推广到模糊数空间,即为模糊随机微分方程.本文用Picard迭代的方法证明了其解的存在唯一性定理,推广了现有文献的结果,并且给出Picard迭代近似解误差的估计式.     

基于模糊传感器的机器人动态障碍环境中的运动控制

对自主式机械手在动态和部分已知且存在运动障碍环境中的运动规划和控制进行了研究,解决了自由碰撞运动控制中具有普遍意义的问题。利用人工势能场的机器人导航控制技术由模糊控制实现,系统的稳定性由李雅普诺夫原理保证。模糊控制器为机器人伺服提供控制指令,使机器人在不可预知的环境中能实时地、自主地选择到达目标的路径和方向。在动态环境的实时控制中,基于传感器的运动控制是处理未知模型和障碍物的重要控制方式。     

A Variational Complex for Difference Equations

An analogue of the Poincaré lemma for exact forms on a lattice is stated and proved. Using this result as a starting-point, a variational complex for difference equations is constructed and is proved to be locally exact. The proof uses homotopy maps, which enable one to calculate Lagrangians for discrete Euler–Lagrange systems. Furthermore, such maps lead to a systematic technique for deriving conservation laws of a given system of difference equations (whether or not it is an Euler–Lagrange system).     

On the Liapunov Second Method for Difference Equations

We study various kinds of stability of a constant solution of an autonomous difference equation by using auxiliary functions like in the Liapunov Second Method. We establish new general principles and we improve several classical results.