基于线性矩阵不等式的广义神经网络系统的全局指数稳定性分析

本文通过构造Lyapunov-Krasovskii泛函并利用线性矩阵不等式的方法将系统的稳定性问题转化为凸优化问题,建立了系统指数稳定的充分条件.该充分条件可利用标准的Matlab LMI工具箱来验证和求解.     

含非线性项的不确定离散时滞系统鲁棒稳定性分析

针对一类同时存在非线性项和不确定项的离散时滞系统,研究了系统的鲁棒稳定性问题.通过构造Lyapunov函数并利用Schur补引理以线性矩阵不等式(LMI)形式给出了系统鲁棒稳定的充分条件;利用离散时滞系统鲁棒稳定性的充分条件,采用LMI技术,设计出基于LMI的状态反馈鲁棒控制器;理论证明该方法设计的控制器保证闭环系统鲁棒渐近稳定.     

一类时滞连续模糊系统稳定性研究

对一类状态时滞连续模糊系统模型稳定性进行了研究,基于Lyapunov稳定性理论证明其系统的稳定性,利用线性矩阵不等式(LMI)方法,得到其稳定的一个充分条件.最后用数值例子进一步说明本文所给方法的有效性.     

广义系统动态输出反馈控制设计的新方法

对于连续时间的广义系统,基于线性矩阵不等式(LMI),提出了动态输出反馈H_∞控制设计的新方法.给出了广义系统动态输出反馈H_∞控制存在的充分条件.通过求解线性矩阵不等式和矩阵方程实现控制的设计.所提出确定控制的方法是简洁和易于实现的.一个数值例子说明了提出方法的设计过程和控制的有效性.     

不确定奇异系统的鲁棒严格无源和ISS（英文）

研究了一类不确定性奇异系统的严格无源和ISS问题.利用线性矩阵不等式(LMI)方法,给出了系统严格无源和ISS的充分条件.当获取的线性矩阵不等式条件不能被满足时,考虑状态反馈问题,并设计有效的控制方法使系统达到相应的性能.最后,通过数值仿真例子验证了本文方法的有效性.     

线性广义时滞系统的H∞输出反馈控制器

本文首先给出了广义时滞系统稳定的一个充分条件，接着讨论了线性广义时滞系统的H∞输出反馈控制，给出了控制器存在的充分条件，同时利用线性矩阵不等式(LMI)的方法，给出控制器的设计，最后举例说明本文方法的可行性．     

基于观测器的非线性不确定时滞跳变系统无源控制

该文基于鲁棒控制理论,采用线性矩阵不等式(LMI)方法,研究了一类非线性不确定时滞Markov跳变系统的无源控制问题,设计了基于观测器的无源控制器.通过构造合适的Lyapunov函数,给出了对所有允许的不确定、时滞和非线性,被控对象满足无源控制指标约束下系统渐近稳定的一个充分条件.求解一个线性矩阵不等式,即可获得系统的无源控制器.仿真示例显示了该文设计方法的有效性.     

基于LMI方法的一类非线性模糊脉冲系统的鲁棒模糊控制

通过推广一般T-S模糊模型定义了一类非线性模糊脉冲系统.基于线性矩阵不等式(LMI)方法提出了一种鲁棒模糊控制新方案.采用并行分布补偿(PDC)的基本思想设计状态反馈控制器,并利用Lyapunov方法理论证明闭环系统全局指数稳定.最后基于LMI方法,将鲁棒模糊控制器的设计问题转化为线性矩阵不等式问题(LMIP).仿真表明本方法的有效性.     

Markovian跳变不确定时滞分布参数系统的鲁棒控制

基于线性矩阵不等式方法对一类含Markovian跳变的不确定时滞分布参数系统的鲁棒控制进行了研究.通过构造恰当的Lyapunov泛函,计算弱无穷小算子,以一组线性矩阵不等式给出系统鲁棒镇定的充分条件.该充分条件易通过Matlab进行求解,方便实际应用.最后,数值例子验证了方法的有效性.     

一类模糊非脆弱静态输出反馈控制器的设计

提出一种离散模糊非脆弱静态输出控制器的设计方法。在控制器增益存在加性摄动的情况下,基于并行分布补偿基本思想(PDC),提出一个判定了闭环离散模糊双线性系统稳定的充分条件。这些充分条件可进一步转化为线性矩阵不等式(LMI)的形式,模糊控制器通过求解线性矩阵不等式得到。仿真实例验证了所提方法的有效性。     

基于LMIs的一类不确定线性切换系统的鲁棒控制

基于LMIs处理方法,研究了一类不确定线性切换系统在任意切换下的鲁棒控制问题.利用矩阵Schur补引理构造线性矩阵不等式,得到该系统的鲁棒稳定性的充要条件,同时也给出了在状态反馈下的鲁棒稳定性充要条件和在输出反馈下的充分条件.最后用数值例子对所得结果加以验证,说明了文中结果的正确性.     

Bounds for eigenvalues using traces

Several new inequalities are obtained for the modulus, the real part, and the imaginary part of a linear combination of the ordered eigenvalues of a square complex matrix. Included are bounds for the condition number, the spread, and the spectral radius. These inequalities involve the trace of a matrix and the trace of its square. Necessary and sufficient conditions for equality are given for each inequality.     

Image Space Analysis for Vector Variational Inequalities with Matrix Inequality Constraints and Applications

In this paper, vector variational inequalities (VVI) with matrix inequality constraints are investigated by using the image space analysis. Linear separation for VVI with matrix inequality constraints is characterized by using the saddle-point conditions of the Lagrangian function. Lagrangian-type necessary and sufficient optimality conditions for VVI with matrix inequality constraints are derived by utilizing the separation theorem. Gap functions for VVI with matrix inequality constraints and weak sharp minimum property for the solutions set of VVI with matrix inequality constraints are also considered. The results obtained above are applied to investigate the Lagrangian-type necessary and sufficient optimality conditions for vector linear semidefinite programming problems as well as VVI with convex quadratic inequality constraints.     

On the set covering polytope: I. All the facets with coefficients in {0, 1, 2}

While the set packing polytope, through its connection with vertex packing, has lent itself to fruitful investigations, little is known about the set covering polytope. We characterize the class of valid inequalities for the set covering polytope with coefficients equal to 0, 1 or 2, and give necessary and sufficient conditions for such an inequality to be minimal and to be facet defining. We show that all inequalities in the above class are contained in the elementary closure of the constraint set, and that 2 is the largest value ofk such that all valid inequalities for the set covering polytope with integer coefficients no greater thank are contained in the elementary closure. We point out a connection between minimal inequalities in the class investigated and certain circulant submatrices of the coefficient matrix. Finally, we discuss conditions for an inequality to cut off a fractional solution to the linear programming relaxation of the set covering problem and to improve the lower bound given by a feasible solution to the dual of the linear programming relaxation.Research supported by the National Science Foundation through grant ECS-8503198 and the Office of Naval Research through contract N0001485-K-0198.     

中立型驱动反应BAM 神经网络的全局渐近同步性

针对一类具有时滞的中立型驱动反应BAM神经网络,提出全局渐近同步性问题.不使用现有文献中传统的李雅普诺夫泛函、矩阵测度和线性矩阵不等式(LMI)等已被广泛应用于研究神经网络全局渐近同步性的方法,而是通过构造2个微分不等式U 1(t)和U 1(t),利用微分不等式方程和不等式技巧解出2个不等式,得到能够确保中立型驱动反应BAM神经网络全局渐近同步的两个新的充分条件.     

General criteria for redundant and nonredundant linear inequalities

A system of linear inequalities subject to nonnegativity restrictions is considered. General criteria which are necessary and sufficient for a linear inequality to be redundant are derived. This general characterization provides a basis for unifying some of the existing techniques. After taking into consideration the existence of redundant linear inequalities, general necessary and sufficient criteria for a linear inequality to be nonredundant are also obtained. An example is given to illustrate the application of these new criteria.The author wishes to thank the referee for his comments.     

Strict anisotropic norm bounded real lemma in terms of matrix inequalities

This paper is aimed at extending the H _∞ Bounded Real Lemma to stochastic systems under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in the terms of information theory using the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is a stochastic counterpart of the H _∞ norm. A state-space sufficient criterion for the anisotropic norm of a linear discrete time invariant system to be bounded by a given threshold value is derived. The resulting Strict Anisotropic Norm Bounded Real Lemma involves an inequality on the determinant of a positive definite matrix and a linear matrix inequality. These convex constraints can be approximated by two linear matrix inequalities.     

Faces for a linear inequality in 0–1 variables

Given a linear inequality in 0–1 variables we attempt to obtain the faces of the integer hull of 0–1 feasible solutions. For the given inequality we specify how faces of a variety of lower-dimensional inequalities can be raised to give full-dimensional faces. In terms of a set, called a “strong cover”, we obtain necessary and sufficient conditions for any inequality with 0–1 coefficients to be a face, and characterize different forms that the integer hull must take. In general the suggested procedures fail to produce the complete integer hull. Special subclasses of inequalities for which all faces can be generated are demonstrated. These include the “matroidal” and “graphic” inequalities, where a count on the number of such inequalities is obtained, and inequalities where all faces can be derived from lower dimensional faces.     

Delay-dependent robust control for uncertain switched systems with time-delay

This paper considers a class of uncertain switched systems with constant time-delay. Based on Krasovskii–Lyapunov functional methods and linear matrix inequality techniques, delay-dependent stability conditions for robust stability and stabilization of the system are derived in terms of linear matrix inequalities. Moreover, dwell time constraints are imposed for the switching law. Some numerical examples are also given to illustrate the results.