摄动离散矩阵Lyapunov方程解的估计

研究摄动离散矩阵Lyapunov方程解的估计问题,利用矩阵运算性质及Lyapunov稳定性理论,给出在结构不确定性假设下方程解的存在条件及解的上下界估计,估计结果由一个线性矩阵不等式(LMI)和两个矩阵代数Riccati方程确定．针对几种不确定性假设,进一步给出矩阵代数Riccati方程的具体形式．最后通过一个算例说明了所得结果的有效性．     

摄动离散LYAPUNOV方程解的上下界估计

给出了离散Lyapunov方程在参数摄动下正定解上、下界的一种新估计,它允许的 摄动结构更为一般,且只需解两个代数Riccati方程,从而避免了高阶代数方程的求解.从而 为基于李雅普诺夫方程的系统分析及控制问题提供必要的理论分析基础.数值算例说明了本 文结果的优越性.     

参数不确定系统的鲁棒H_∞估计

从代数Riccati不等式 (ARI)设计H∞ 控制问题出发 ,通过选取参数矩阵M和N ,对鲁棒H∞ 估计器的代数Riccati不等式进行简化 .再根据Schur补公式 ,导出用线性矩阵不等式设计鲁棒H∞ 估计器的定理 .例子说明设计的估计器具有很好的鲁棒性     

求解规范型Lyapunov矩阵方程的新方法

本文揭示了规范型Lyapunov矩阵方程及其对偶方程的一些特殊性质,充分压缩解矩阵的未知元素,并利用对偶解矩阵与解矩阵的合同关系,提出了一种高精度、高效率求解规范型Lyapunov方程的新算法,文中举例验证了新算法的正确性。 Lyapunov矩阵方程 能控制和能观测规范型 单输入单输出系统     

基于类二次型Lyapunov函数的Super-twisting算法收敛性分析

基于非光滑的类二次型Lyapunov函数,对二阶滑模Supevtwisfing算法的有限时间收敛性进行了分析．当系统受常值干扰时,通过Lyapunov方程证明了该算法有限时间收敛,并给出了收敛时间的最优估计;当系统受时变干扰时,通过求解代数Riccati方程得出了一组保证该算法有限时间收敛的参数取值范围,并给出了收敛时...     

一种对错误匹配点鲁棒的多单应矩阵估计方法

针对错误匹配点干扰条件下的多单应矩阵估计问题,提出了一种对错误匹配点鲁棒的多单应矩阵估计初始化方法.该方法基于特征点对的代数误差和结构相似性约束条件,将错误匹配点剔除策略有机地融合到单应矩阵估计的过程中,在不增加计算复杂度的前提下,能够有效地剔除错误匹配点并估计出多单应矩阵的初值.结合AML-COV(approximate maximum likelihood with homography covariance)后端优化算法,本文通过仿真数据实验和真实图像实验从客观性能指标和主观视觉效果方面对算法的性能进行了验证分析.实验结果表明,本文提出的多单应矩阵估计方法能够精确、高效、鲁棒地估计出多单应矩阵的值,较好地解决了错误匹配点干扰条件下的多单应矩阵估计问题.     

一类关联时滞系统的分散稳定化控制器设计

应用Lyapunov稳定性理论,提出一类关联时滞系统能用分散线性状态反馈镇定的充分条件,进而证明了该条件等价于子系统级上N个带参数的代数Riccati矩阵方程的正定解的存在性,并利用这些正定解矩阵给出了相应的稳定化分散控制器。应用所提出的方法,可望得到具有更小反馈增益参数的分散稳定化控制律。     

大型Lyapunov方程的并行求解

借鉴于求解大型矩阵主特征对方法中子空间迭代的概念,给出了求解Lyapunov方程的 新方法,进而推导出Lyapunov方程直接迭代的高效并行算法,同时也给出了算法的收敛性证 明和解的误差分析.     

区域极点配置问题的研究方法

对区域极点配置的现有研究成果进行综述.将区域极点配置的基本方法归结为代数Riccati方程(ARE)方法和线性矩阵不等式(LMI)方法.列出了基于区域极点配置方法的主要研究成果,包括最优控制、鲁棒性、H2性能、H∞性能等方面.最后给出了几点研究展望.     

基于一般Lur''''e系统的混沌同步研究

许多混沌系统可以转化为一个Lur'e系统.本文采用时滞反馈控制技术研究了一般Lur’e系统的混沌同步问题,改进了最近有关文献的结果.通过利用Lyapunov—Krasovskii函数法得到了时滞无关的线性矩阵不等式(LMI)判据,而且还通过利用M-矩阵等方法,得到了易于检验的时滞相关与时滞无关的代数判据,利用这些结果给出了这种反馈控制器的设计方法;最后,给出的例子阐明了所得到的结果.     

Unified type non-stationary Lyapunov matrix equation — Simultaneous eigenvalue bounds

Simultaneous eigenvalue bounds for the solution of the unified non-stationary Lyapunov matrix equation are presented. When the solution becomes stationary, the results reduce to bounds of the unified type algebraic Lyapunov equation. In the limiting cases, the results reduce to bounds for the solution of the differential and difference Lyapunov equations. The bounds given in this paper are a generalization of some existing bounds obtained separately for the continuous and discrete type stationary and non-stationary Lyapunov equations.     

Delta 域Riccati方程研究：连续与离散的统一方法

基于Ｄｅｌｔａ算子研究连续Ｒｉｃｃａｔｉ方程和离散Ｒｉｃｃａｔｉ方程的统一形式,得到Ｄｅｌｔａ域Ｒｉｃｃａｔｉ方程解的定界估计,本文结果与现有的结果相比,具有较小的保守性,在极限情形下可分别得到连续和离散Ｒｉｃｃａｔｉ方程的相关结论。     

Bounds for the eigenvalues of the solution of the unified algebraic Riccati matrix equation

In recent years, several eigenvalues bounds have been investigated separately for the solutions of the continuous and the discrete Riccati and Lyapunov matrix equations. In this paper, lower bounds for the eigenvalues of the solution of the unified Riccati equation (relatively to continuous and discrete cases), are presented. In the limiting cases, the results reduce to some new bounds for both the continuous and discrete Riccati equation.     

Bounds for the eigenvalues of the solution of the discrete Riccati and Lyapunov equations and the continuous Lyapunov equation

We present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapunov matrix equation. Nearly all of our bounds for the discrete Riccati equation are new. The bounds for the discrete and continuous Lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation.     

Bounds for the solution of the Lyapunov matrix equation — A unified approach

In recent years, several bounds have been reported for the solution of the continuous and the discrete Lyapunov equations. Using the unified Lyapunov equation, we give in this paper bounds for the solution of this equation. In the limiting cases, the bounds reduce to existing bounds for both the continuous and discrete Lyapunov equations.     

Matrix bounds of the discrete ARE solution

This paper provides new lower and upper matrix bounds of the solution to the discrete algebraic Riccati equation. The lower bound always works if the solution exists. The upper bounds are presented in terms of the solution of the discrete Lyapunov equation and its upper matrix bound. The upper bounds are always calculated if the solution of the Lyapunov equation exists. A numerical example shows that the new bounds are tighter than previous results in many cases.     

Matrix bounds of the solutions of the continuous and discrete Riccati equations--a unified approach

In this paper, a new scheme is introduced to measure the matrix bounds of the continuous and discrete Riccati equations. By estimating upper and lower matrix bounds of the solution of the unified algebraic Riccati equation (UARE), the same measurements for the solutions of the continuous and discrete Riccati equations, respectively, can be obtained in limiting cases. According to these obtained matrix bounds, several eigenvalue bounds are also defined. All the proposed results for the UARE are new and more general than previous work. Some obtained results are compared with those of the literature. Via numerical examples, it is shown that in some cases the presented results are tighter than the existing ones.     

New results for the bounds of the solution for the continuousRiccati and Lyapunov equations

This paper presents upper and lower matrix bounds for the solution of the continuous algebraic matrix Riccati equation. Furthermore, a new lower matrix bound for the solution of the continuous algebraic Lyapunov equation is also developed. These are new results     

Upper bounds for the eigenvalues of the solution of the discretealgebraic Lyapunov equation

Upper bounds for summations including the trace, and for products including the determinant, of the eigenvalues of the solution of the discrete algebraic Lyapunov equation (DALE) are presented. All bounds are derived from the matrix series solution of the DALE. The majority of the bounds are tighter than those in the literature     

Lower bounds for the solution of the discrete algebraic Lyapunovequation

Lower bounds for the determinant and for the trace of the matrix solution of the discrete algebraic Lyapunov equation are presented. The determinant is tighter than bounds in the literature, and the trace supplements them