具有Frobenius范数界的不确定广义系统鲁棒二次稳定完整性

考虑带有Frobenius范数界的不确定广义系统具有完整性的鲁棒二次稳定问题.通过代数Riccati不等式给出不确定广义系统在状态反馈下所构成的闭环系统鲁棒二次稳定并且当执行器出现故障时不确定广义系统仍能保持鲁棒二次稳定的充分条件,即不确定广义系统具有完整性的充分条件,最后用数学例子说明本方法的有效性.

一类Hermite插值算子的C^1—范数界

本文给出一类以(1-X^2)U_n(X)(U_n(X)是第二类 Chebyshev 多项式)的零点为节点的 Hermite 插值算子的 C^1—范数的上下界,得到(2/π)|(1/n+1)sin(π/(4(n+1)))+(-1)~n cos(π/4(n+1))|1n(2n+1)-1-(1/2(n+1))tg(π4(n+1))≤‖H_(2n+3)‖≤(175/3)

线性模型中均值向量的最小二乘估计和最佳线性无偏估计之差的范数界的注记

我们讨论一般线性模型:Y=Xβ+e,E(e)=0,Cov(e)=σ~2V,V为非负定协方差矩阵。我们知道μ=Xβ的最小二乘估计和最佳线性无偏估计分别为μ~*=X(X′X)^-X′Y和■=X(X′T^-X)^-X′X^-Y,这里T=V+XUX′,U是一个对称阵使得R(T)=R(V■X)以及T≥0。本文讨论V≥0时,■与μ~*之差的范数界,把V>0时■和μ~*之差在Haberman条件下的范数界推广到V≥0,且在取常用的欧氏范数时,得到使Haberman条件成立的便于应用的充要条件。本文还证明了[2]界的推广形式,并把[3]界推广到V≥0的情况。

状态滞后线性系统的H_∞ 状态反馈控制器(英文)

利用LMI(线性矩阵不等式 )的方法 ,首先给出了一般的状态滞后自治系统内稳定且具有H∞ 范数界的一个充分条件 .并由此得到了一般的状态滞后系统H∞ 问题有解的一个充分条件 ,通过解LMI可以获得控制器的解 .最后举例说明方法的正确性 .

传感器失效的飞控系统完整性控制器设计

从提高新一代战斗机可靠性和性能出发,提出对飞控系统传感器失效具有完整性的鲁棒容错控制器设计方法。采用状态观测器理论和H∞鲁棒控制理论相结合的方法,针对已知故障设计的控制器,在传感器正常和故障两种情况下,既保证闭环系统的鲁棒稳定性,又保证了闭环系统对于外界干扰具有要求的H∞范数指标。以某型战斗机为算例,考虑俯仰角速率传感器失效和阵风干扰,进行控制器设计,仿真结果验证该方法的正确性和有效性。

具有多步随机延迟和参数不确定动态系统的滤波器设计（英文）

针对一类传感器观测具有多步随机延迟、状态转移矩阵具有范数界不确定的离散动态系统,在Minmax准则下设计了一种最优的滤波器。对于这类问题,已有的方法主要限于一步随机延迟的情况,通过最小化估计误差协方差矩阵的某种上界来设计滤波器,在递推算法中每一步都需要给定一个尺度参数;而改进滤波算法在实际应用中更加方便。通过数值例子表明,对于具有一步延迟的传感器观测,与已有方法相比该方法具有更小的平均估计误差;同时,对于两步随机延迟的动态系统也具有较好的滤波效果。

广义不确定时滞系统的可二次镇定性

着重讨论了一类广义不确定时滞系统的鲁棒控制问题,给出了对容许不确定性,系统可二次镇定和满足从干扰输入到控制输出的H∞范数界约束的无记忆状态反馈鲁棒H∞控制的分析结果,得到了H∞范数界约束下广义不确定时滞系统可二次镇定的充分条件。

Upper Bounds for the L_p-norms of the Maximal Functions of Martingales

Let 2≤p【∞ and let (f n) be a martingale. Using exponential bounds of the probabilities of the type P(|f n|】λ‖T(f n)‖ ∞) for some quasi-linear operators acting on martingales, we estimate upper bounds for the L p-norms of the maximal functions of martinglaes. Our result is the extension and improvements of the results obtained previously by HITCZENKO and ZENG .

Analyzing Influencing Factors of Rural Poverty in Typical Poverty Areas of Hainan Province: A Case Study of Lingao County

Rural poverty and poverty reduction are not only the focal issues that have attracted worldwide attention, but also the vital issues on people's livelihood that has attached great importance and aimed to be solved by the central and local governments of China. Based on the survey data of 354 farming households, this paper, taking the national poverty county of Lingao County, Hainan Province for an example, examined the characteristics of rural poverty of the county. Moreover, this paper established the spatial lag model(SLM) from five dimensions, namely, status of the household head, household structure, health status, income composition and traffic accessibility, to analyze the main influencing factors of rural poverty according to the values of Moran's I and the diagnosis of spatial dependence of the OLS model. It is found that the poor farming households gathered mainly in five towns in the north and southwest of the county, and the rural poverty have the characteristics of low educational level of the heads, more minor children, high population of farming peasants, high incidence of disease and low proportion of household wage-equivalent income. The results also showed that the variables such as the number of minor children, the number of migrant worker, the number of farming peasants and the proportion of wage-equivalent income have significant effectiveness on rural poverty, while the status of the household head, health status and traffic accessibility have little influence. It is an important way to realize the goal of poverty alleviation by controlling the number of farmers' fertility, strengthening the vocational skills training of farmers, vigorously developing specialization and large-scale agriculture and increasing the employment opportunities of farmers.

Probabilistic Norm of Operators and Continuity of Bounded Operators

In this paper,the equivalence for continuity and boundedness of the linear operators on a general PN space is proved by means of their probabilistic norm,and the corresponding result in [1] is improved.

Robust H_∞ filtering for neutral jump system with time-delays and uncertainties

The problem of robust H∞ filtering for a class of neutral jump systems with time-delay and norm- bounded uncertainties is considered. By re-constructing the system, the dynamics of overall augmented error systems is obtained which involves unknown inputs represented by disturbances, model uncertainties and time-delays. As to the nominal system, sufficient conditions are provided for the existence of the mode-dependent H∞ filter by selecting the appropriate Lyapunov-Krasovskii function and the robust H∞ filter is proposed for the jump system while considering the time-delays and uncertainties. Both of above conditions for the existence of the H∞ filter and roust H∞ filter are presented in terms of linear matrix inequalities, and convex optimization problems are formulated to design the desired filters. By employing the proposed mode-dependent H∞ filter, the systems have the stochastic stability and better ability of restraining disturbances stochastically, and the given prescribed H∞ performance is guaranteed. Simulation resuhs illustrate the effectiveness of developed techniques.

Nonconforming Finite Element Method for Gradient flow Equations in Robin Conditions

In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogonality of this element＇s basic functions, the convergence analysis for L2-norm and broken H1-norm with semi-implicit scheme is presented. And the error order is improved to the optimal, too.

An Upper Bound of Essential Norm of Composition Operator on H^2(B_n)

The authors give an upper bound of the essential norm of a composition operator on H2(Bn),which involves the counting function in the higher dimensional value distribution theory defined by S.S.Chern.A criterion is also given to assure that the composition operator on H2(Bn) is bounded or compact.

Global Well-Posedness and Scattering for the Defocusing H^s-Critical NLS

The authors consider the scattering phenomena of the defocusing H^s-critical NLS.It is shown that if a solution of the defocusing NLS remains bounded in the critical homogeneous Sobolev norm on its maximal interval of existence,then the solution is global and scatters.

Robustness properties of dimensionality reduction with Gaussian random matrices

In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property(RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.

An Upper Bound of Fully Entangled Fraction of Mixed States

We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.

LOCAL SPECTRA OF UNILATERAL OPERATOR WEIGHTED SHIFTS

In this note, the local spectral properties of unilateral operator weighted shifts are studied.

Spectral Inclusion Properties of Unbounded Hamiltonian Operators

In this paper, the authors investigate the spectral inclusion properties of the quadratic numerical range for unbounded Hamiltonian operators. Moreover, some examples are presented to illustrate the main results.