一类基于观测器的线性不确定系统的正实控制

本文考虑了一类基于观测器的线性不确定系统的正实控制问题，其中它的不确定性更具一般性．把这类问题转化为带有常量参数的系统的正实控制问题，通过求解线性矩阵不等式得到控制器参数的解，设计的此类基于观测器的控制器，使得闭环系统稳定且扩展严格正实．最后通过仿真算例进一步验证了该控制方案的有效性．     

一般非线性变分不等式组的两步投影算法

对一类新的包含两个不同非线性算子的一般变分不等式组进行了研究；利用投影技巧，给出了一个求解这种一般变分不等式组的显式两步迭代算法；证明了该算法在适当的条件下收敛；所得的结果改进了该领域内的一些最新结果．     

A Combined Feasible-Nonfeasible Point Continuation Method for Strongly Monotone Variational Inequalities

IntroductionWeconsidertilefollowingvariationalinequalityproblelll(VIPforshort)wllicllistofillfiavectorx*eXsuchthatVIP(X,F)F(X*)"(X~X.)Z0VXEX.(1)wiler(iF:R;;-R"isagivenfllllctiollandXCRniscalls(1tilefeasiblesetofVIP(X.F)ItiswellknownthatVIPisaveryilnportalltrcsearcllareasillceit11dsllumerousapl)licatiollsinbothmatllelllaticsitselfalldecollonlics.Mailysocialalldeconomiclllodels,collvexluathelnaticalprogranullillgsandsooncanbecollsideredasspecialcasesofVIP,tile"lorecollcreteapplicit…     

Delay-dependent state feedback robust stabilization for uncertain singular time-delay systems

The problem of robust stabilization for uncertain singular time-delay systems is studied.First,a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given,which is less conservative.Using this result,the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed.Finally,two examples are given to illustrate the effectiveness of the results.     

用不等式求解一类非线性规划问题

本文在 Bellman 提出的最优化原理的理论基础上,以几种常用的不等式为工具,解一类具有递归型式的非线性规划问题。此法回避了解析法中多维分析的复杂性,使问题得到简化。     

一类三阶微分方程的非线性三点边值问题

研究一定条件下的三阶微分方程的非线性三点边值问题的微分不等式理论与解的存在性.     

Witten复形与Morse不等式

本文用分析的方法利用Ｗｉｔｔｅｎ复形证明了非退化的Ｍｏｒｓｅ不等式，极大，极小的方法被用来估计Ｗｉｔｔｅｎ形变的Ｌａｐｌａｃｅ的小特征值。     

Non-fragile decentralized H∞ controller design for uncertain linear systems

Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized H∞ controllers guarantee that the uncertain closed-loop linear systems are stable and with H∞ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile H∞ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.     

关于两类积分不等式的推广及其在稳定性理论中的应用

建立和改进了两类积分不等式．     

AN EXPONENTIAL INEQUALITY FOR AUTOREGRESSIVE PROCESSES IN ADAPTIVE TRACKING

A wide range of literature concerning classical asymptotic properties for linear models with adaptive control is available, such as strong laws of large numbers or central limit theorems. Unfortunately, in contrast with the situation without control, it appears to be impossible to find sharp asymptotic or nonasymptotic properties such as large deviation principles or exponential inequalities. Our purpose is to provide a first step towards that direction by proving a very simple exponential inequality for the standard least squares estimator of the unknown parameter of Gaussian autoregressive process in adaptive tracking.