基于谱分解的中立型时滞系统观测器

针对线性中立型时滞系统, 利用线性算子半群的谱分解理论进行观测器设计. 在中立型项的范数小于一的条件下, 利用谱理论并结合投影算子, 将无穷维系统解的相空间分解为有限维不稳定广义特征子空间和无限维稳定广义特征子空间的直和. 进而利用线性算子半群的无穷小生成元得到具有积分微分形式的观测器方程, 并证明了观测器误差方程的渐近稳定性. 数值实验证实了所提设计方法的有效性.     

Intuitionistic fuzzy transformation semigroups

The idea of (faithful) intuitionistic fuzzy transformation semigroup, intuitionistic admissible relation, and intuitionistic (strong) homomorphism are introduced and their basic properties are examined.     

Approximate controllability of linear retarded systems in Hilbert spaces

The object of this paper is to construct some results on the control problems for retarded functional differential equations of parabolic type with unbounded principal operators in Hilbert spaces. In order to establish relations between controllability of the given equation and observability of the adjoint system, we investigate the equivalent relation for the completeness of generalised eigenspaces of the infinitesimal generators. Finally, when the control space is a finite-dimensional space, a necessary and sufficient condition for the approximate controllability of retarded equations is given by the so-called rank condition.     

Approximate controllability of partial neutral functional differential systems of fractional order with state-dependent delay

We prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the Krasnoselskii–Schaefer type fixed point theorem with the fractional power of operators. An example is provided to illustrate the main results.     

关于逆半群的几个注记

研究了逆半群在自然偏序下的最小群同余结构,刻画了逆牛群的R一类的半格,证明了满足极小条件min_R的逆半群S关于最小群同余的商S/σ同构于S的一个一类。     

抽象泛函微分方程的最大解和最小解

本文利用增算子不动点定理讨论了抽象泛函微分方程的最大解和最小解,得到了迭代公式,并把结果应用于偏泛函微分方程。     

确定局部结构已知的半群的一种算法

给出了确定局部结构已知的有限半群的推理法则，提出了一种新的计算机算法。     

关于一类偏序正则半群

给出了上半格偏序正则半群的定义.通过对其偏序的研究,得到上半格偏序正则半群成为逆半群的一个刻画.设(S,V,·,≤)是上半格偏序正则半群,若≤是自然偏序≤的扩张,则(S,·)是逆半群.进一步地,若≤是amenable偏序,则(S,·)是Clifford半群.     

关于左C-wrpp半群的若干性质

左C-wrpp半群是左C-半群和左C-rpp半群的共同推广,杜兰等研究了左C-wrpp半群,给出了左C-wrpp半群的curler结构。进一步研究左C-wrpp半群,得到左C-wrpp半群的若干特征和等价刻画,丰富了杜兰等关于左C-wrpp半群的结果。     

序半群上的等同关系

首先引入了Quantale上两个子集之间的等同关系;其次,利用序半群的Quantale完备化给出了序半群上两个子集之间的等同关系;最后,讨论了序半群上三个不同等同关系的性质。