A∞∞ _ 型 Ringel-Hall 代数

这是利用 A^∞_∞ -型 Ringel-Hall 代数研究sl ^∞_∞ -型量子群的两篇文章中的第一篇. 为此首先需要研究建立在任意域k 上的无限维路代数 kA^∞_∞ 的有限维表示. 在文章的第一部分, 我们给出了所有的不可分解 kA^∞_∞ - 表示, 并且清楚地刻画了它们之间的扩张关系; 在第二部分, 对于给定的有限域k, 我们研究了 Ringel-Hall 代数 H(kA^∞_∞). 主要观察是把H(kA^∞_∞) 看作 Ringel-Hall 代数 H(kA_∞) 的正向极限, 把 H(kA_∞) 看作Ringel-Hall 代数 H(kA_n) 的正向极限. 特别地, 我们得到了H(kA^∞_∞) 的一个 PBW-基, 并且 证明了H(kA^∞_∞) 恰好和它的合成子代数重合.     

Hilbert变换相关的分布空间及其应用

本文构造了一个新的分布空间D′_H, 并且把经典的Hilbert变换的定义 推广到这个空间上. 证明了推广的Hilbert变换是把空间D′_H映射到自身的 同胚映射, 且D′_H是满足该条件的D′的最大子空间. 进一步, 证明了L^p空间中经典的Hilbert变换和周期函数空间中周期Hilbert变换都是这一推广Hilbert变换的特款. 对空间D_H的性质进行了刻画, 并给出了空间D′_H中的一类非常有用的非线性相位信号. 最后给出了该推广Hilbert变换的两个简单的应用.     

Fτ-Coherent 风险度量

该文提出了一个风险度量的新概念,即定义在任意停时 τ上的 F_τ-Coherent 风险度量. 对任一 满足Fatou 性质的F_τ-Coherent 风险调整值度量(即一个F_τCoherent风险度量的负值) ф_т: L^∞ (F) →L^∞ (F_τ) 我们都可以用一个 F_τ-凸概率测度集来给出它的显式表示.同时我们还证明了一个 F_τ-Coherent 风险调整值度量可以用它的可接受头寸集合来表示.     

重图的超f - 边覆盖染色

图G的一个超f - 边覆盖染色就是它的一个f - 边覆盖染色并且使得图G中的重边染上不同的颜色. 令χ^H_fc(G)是图G存在一个超f - 边覆盖染色时所需最大的颜色数k. χ^H_fc(G)称作是图G的超f - 边覆盖染色色数. 本文讨论重图的超f - 边覆盖染色的存在性并且给出了重图的超f - 边覆盖染色的色数下界.     

QK空间的插值序列

本文研究了Q_K空间的插值问题.利用复分析和调和分析的方法,获得了单位圆盘上的一个序列{z_n}是Q_K∩H^∞空间的插值序列的一个充分必要条件,推广了Q_p空间的部分结果.     

α -正规函数的一些积分准则

对 0<α <∞, N^α 是开单位圆盘 D 上满足 sup _{z∈ D}(1-|z|²)^α f^# (z)<∞ 的亚纯函数类, 其中 f^# (z)=|f'(z)|/(1+|f(z)|²) 是 f 的球面导数. 该文给出了 D 上的 α -正规函数类的一些积分准则, 并用 Bergman-Carleson 测度的形式予以表示.     

指数多项式在半带形中的闭包

该文对一类复指数多项式组成的线性空间$M(\Lambda )$ 在Banach 空间 H_α中的不完备性给出了充分必要条件, 其中 H_α为在半带形 I_α={z=x+iy: x≥ 0, |y|≤α} (α > 0 )中连续, 在I_α的内部解析且当 x→∞时, f(x+ iy)在I_α中关于 y 一致地 趋向 0 的函数 f(x+ iy)全体, 其范数为上确界范数. 同时指出, 如果$M(\Lambda )$ 在 H_α中不完备, 则它的闭包cl$(M(\Lambda ))$中所有的函数都可以延拓为由Dirichlet级数表示的解析函数.     

关于(f,τ) -相容Hopf代数对(B,H)

该文定义了(f,τ) -相容Hopf代数对(B,H),利用这样的对(B,H),给出了左H -余模范畴^HM的一个辫子张量子范畴,从而得到一个量子Yang-Baxter算子,并且通过扭曲Hopf代数$B$的乘法,构造出Yetter-Drinfeld范畴中^H_HYD的Hopf代数.     

Hilbert空间上线性算子广义逆A(2)T,S的存在性及其表示式

设H₁和H₂是两个Hilbert空间, B(H₁,H₂)表示从H₁到H₂的所有有界线性算子的集合, T和S分别是H₁和H₂的两个闭子空间. 如果存在线性算子X ∈ B(H₂,H₁)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A⁽²⁾_T,S. 该文进一步研究了线性算子广义逆A⁽²⁾_T,S存在的若干等价条件及其性质,建立了算子广义逆A⁽²⁾_T,S的表示形式.     

G-旋模型观测量代数间的C*-指标

在取值于有限群G的二维格子旋系统模型中, 可以定义场代数F. 群G的Double代数D(G), 进而由子群H决定的子Hopf代数D(G;H), 在F上有自然作用, 使得F成为模代数. 给出F的D(G; H)-不变子空间A_H的具体结构, 通过构造A_H到A_G的条件期望γ_G的拟基, 得到γ_G的C^*-指标, 等于子群H在G中的指标.     

Dissipative analysis for discrete‐time systems via fault‐tolerant control against actuator failures

This article investigates the problem of robust dissipative fault‐tolerant control for discrete‐time systems with actuator failures. Based on the Lyapunov technique and linear matrix inequality (LMI) approach, a set of delay‐dependent sufficient conditions is developed for achieving the required result. A design scheme for the state‐feedback reliable dissipative controller is established in terms LMIs which can guarantee the asymptotic stability and dissipativity of the resulting closed‐loop system with actuator failures. In addition, the proposed controller not only stabilize the fault‐free system but also to guarantee an acceptable performance of the faulty system. Also as special cases, robust H_∞ control, passivity control, and mixed H_∞ and passivity control with the prescribed performances under given constraints can be obtained for the considered systems. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault‐tolerant control technique. © 2016 Wiley Periodicals, Inc. Complexity 21: 579–592, 2016     

Observer-based reliable exponential stabilization and H∞ control for switched systems with faulty actuators: An average dwell time approach

This paper deals with the problem of reliable stabilization and $H_{\infty }$ control for a class of continuous-time switched Lipschitz nonlinear systems with actuator failures. We consider the case that actuators suffer “serious failure”—the never failed actuators cannot stabilize the given system. The differential mean value theorem (DMVT) allows transforming the switched Lipschitz nonlinear systems into switched linear parameter varying (LPV) systems. Based on average dwell time scheme and under the condition that activation time ratio between stabilizable subsystems and unstabilizable ones is not less than a specified constant, sufficient conditions for reliable exponential stabilization of the switched systems are derived by hybrid observer-based output feedback control. The result is also extended to the reliable $H_{\infty }$ control problem.     

Robust reliable L2 – L∞ control for continuous‐time systems with nonlinear actuator failures

This article examines the reliable L₂ – L_∞ control design problem for a class of continuous‐time linear systems subject to external disturbances and mixed actuator failures via input delay approach. Also, due to the occurrence of nonlinear circumstances in the control input, a more generalized and practical actuator fault model containing both linear and nonlinear terms is constructed to the addressed control system. Our attention is focused on the design of the robust state feedback reliable sampled‐data controller that guarantees the robust asymptotic stability of the resulting closed‐loop system with an L₂ – L_∞ prescribed performance level γ > 0, for all the possible actuator failure cases. For this purpose, by constructing an appropriate Lyapunov–Krasovskii functional (LKF) and utilizing few integral inequality techniques, some novel sufficient stabilization conditions in terms of linear matrix inequalities (LMIs) are established for the considered system. Moreover, the established stabilizability conditions pave the way for designing the robust reliable sampled‐data controller as the solution to a set of LMIs. Finally, as an example, a wheeled mobile robot trailer model is considered to illustrate the effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 309–319, 2016     

Robust L ∞ reliable control for impulsive switched nonlinear systems with state delay

This paper investigates the problem of robust L _∞ reliable control for a class of uncertain impulsive switched nonlinear systems with time-delay in the presence of actuator failure. Based on the dwell time approach, we firstly obtain a sufficient condition of exponential stability for the impulsive switched nonlinear system with time-delay, and L _∞ performance for the considered system is also analyzed. Then, based on above results, a state feedback controller, which guarantees the exponential stability with L _∞ performance of the corresponding closed-loop system, is constructed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.     

Reliable gain‐scheduled control design for networked control systems

In this article, the problem of reliable gain‐scheduled H_∞ performance optimization and controller design for a class of discrete‐time networked control system (NCS) is discussed. The main aim of this work is to design a gain‐scheduled controller, which consists of not only the constant parameters but also the time‐varying parameter such that NCS is asymptotically stable. In particular, the proposed gain‐scheduled controller is not only based on fixed gains but also the measured time‐varying parameter. Further, the result is extended to obtain a robust reliable gain‐scheduled H_∞ control by considering both unknown disturbances and linear fractional transformation parametric uncertainties in the system model. By constructing a parameter‐dependent Lyapunov–Krasovskii functional, a new set of sufficient conditions are obtained in terms of linear matrix inequalities (LMIs). The existence conditions for controllers are formulated in the form of LMIs, and the controller design is cast into a convex optimization problem subject to LMI constraints. Finally, a numerical example based on a station‐keeping satellite system is given to demonstrate the effectiveness and applicability of the proposed reliable control law. © 2014 Wiley Periodicals, Inc. Complexity 21: 214–228, 2015     

Robust reliable H∞ control for neural networks with mixed time delays

This paper considers the problem of robust reliable H_∞ control for neural networks. The system has time-varying delays, parametric uncertainties and faulty actuators. The faulty actuators are considered as a disturbance signal to the system which is augmented with system disturbance input. Based on the LMI technique and the Lyapunov stability theory, a new set of sufficient conditions is obtained for the existence of the robust reliable H_∞ controller. An example is also presented illustrate the results.     

Robust H{infty} control of uncertain systems with time-varying state and control input delays

In this paper, a new method for robust H controller of uncertainsystems with time-varying state and control input delays isproposed. A sufficient condition, which is dependent on themaximum value of the time derivative of time-varying delay,is also presented for the existence of H controller. The proposedcontroller not only stabilizes closed-loop uncertain systemsbut also guarantees a prescribed H norm bound of the closed-looptransfer matrix from the disturbance to controlled output. Furthermore,we propose a new robust stability criterion to decide the allowedmaximum bound of plant uncertainty which still can be stabilizedby proposed robust controller. An example given illustratesthe availability of the proposed design method.     

不确定线性系统的最优保性能可靠控制

针对一类不确定线性系统,采用连续增益故障模型提出了考虑执行器故障的保性能可靠控制问题.通过对具有执行器增益故障的系统分析,利用线性矩阵不等式(LMI)分别给出了保性能标准控制、最优保性能标准控制、保性能可靠控制、最优保性能可靠控制存在的充分条件.根据凸优化理论,最优保性能标准控制和最优保性能可靠控制的设计方法转化为一个线性凸优化算法.仿真数例验证了文中所提出方法的可行性.在相同形式的故障发生时,比较最优保性能标准控制与最优保性能可靠控制,进一步说明了最优保性能可靠控制的必要性.