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．     

求解弱非比例阻尼系统实模态解的阻尼矩阵摄动法

提出了一种求解弱非比例阻尼振动系统实模态解的摄动方法和将非比拟阻尼矩阵分解为比例阻尼矩阵和余项阻尼矩阵的方法.对于弱非比例阻尼振动系统,通过同时对阻尼矩阵和响应矢量进行小参数摄动,将原非比例阻尼系统分解为一系列的比例阻尼振动系统,在此基础上用正则模态变换将各阶比例阻尼的摄动方程解耦,从而求得原非比例阻尼振动系统的近似解析解.计算实例表明,此方法的结果与数值计算结果十分吻合.     

能控性不变的参数摄动区间的一种估计

本文给出了线性定常系统状态矩阵摄动时保持能控性不变的摄动区间的估计。     

线性时变系统的稳定性

本文介绍线性时变系统方程解的估计问题。根据系统方程系数矩阵Ａ，给出一种方法找出方程解的上边界和下边界。而这种方法与方程的精确解是完全一致的。然后建立线性时变系统稳定性判据。     

D—稳定多项式的球形摄动界

研究了D－稳定多项式的球形摄动界。利用系数空间中距离的概念，给出D－稳定多项式在系数空间中球形摄动界的估计式。对于线性及仿射参数化的D－稳定多项式，讨论了参数空间中参数的摄动，并给出D－稳定多项式在参数空间球形摄动界的估计式。     

D－稳定多项式的球形摄动界

研究了Ｄ－稳定多项式的球形摄动界。利用系数空间中距离的概念，给出Ｄ－稳定多项式在系数空间中球形摄动界的估计式。对于线性及仿射参数化的Ｄ－稳定多项式，讨论了参数空间中参数的摄动，并给出Ｄ－稳定多项式在参数空间球形摄动界的估计式。     

鲁棒稳定性和鲁棒对角优势的关系

本文研究了多输入多输出系统的鲁棒稳定性和鲁棒对角优势的关系.不仅给出了使系统 鲁棒对角优势所需的鲁棒稳定性条件,而且还得出了系统鲁棒对角优势一定保证系统鲁棒稳 定这个一般性的结论.并可根据本文所给的结果,对允许摄动的最大边界进行估计,包括非结 构摄动的范数上界和结构性摄动的摄动矩阵的各元素的模的估计.本文得出的鲁棒对角优势 保证鲁棒稳定的结果是较少保守性的.     

一种参数摄动范围未知系统的鲁棒估计方法

好于具有参数摄动但其摄动范围未知的动态系统的状态估计问题,通过对参数摄动归并到扰动中,则可作为确定性系统对待,由此得出的Ｒｉｃｃａｔｉ不等式是和一些常数有关的,若此Ｒｉｃｃａｔｉ不等式存在的正定对称解,则可参数化状态估计器增益矩阵,计算实例表明,当参数摄动范围未知时,这是一种有效的设计方法。     

鲁里叶系统鲁棒输入输出稳定性的H∞范数摄动界

讨论了一般鲁里叶系统的鲁棒输入、输出稳定性问题.利用H∞范数与互质因子摄 动两种度量方法给出了鲁里叶系统在线性部分与非线性部分同时有摄动时,系统仍能保持输 入、输出稳定性的摄动量上界估计式,并用两个例子说明了该摄动界的有效性.     

非线性奇摄动系统的小增益增长条件

给出小增益增长条件使得在此条件下快慢子系统的渐近稳定性能够保证其原奇摄动系统的相应稳定性,并给出估计摄动参数的稳定界的解析表示及其应用例子.     

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.     

Decision theoretic approach to real-time robust identification

A decision-theoretic approach to the estimation of unknown parameters from a linear discrete-time dynamic measurement model in the presence of disturbance uncertainty is considered. The unknown disturbance statistics are characterized by a certain class of distributions to which the real disturbance distribution is confined. Using game theory and the asymptotic estimation error covariance matrix as the criteria of how good an estimator is, the stochastic gradient-type algorithm is shown to be optimal in the min-max sense. Since the optimal solution is not tractable in practice, several suboptimal procedures are derived on the basis of suitable approximations. The convergence of the derived algorithms is established theoretically using the ordinary differential equation approach. Monte Carlo simulation results are presented for the quantitative performance evaluation of the algorithms.     

线性离散时变系统的状态和输入混合估计: 一种对策方法

本文研究了线性离散时变系统的混合估计问题, 估计信号是状态和输入的线性组合. 设计目标要求满足一个最坏性能指标, 即从扰动到估计误差的能量增益小于一个给定值. 混合估计问题的最优解是二人零和微分对策的鞍点解. 基于微分对策方法, 混合估计问题有解的充要条件表达为 Riccati 微分方程的可解性. 在问题有解时, 给出了符合要求的估计器. 估计器的结构表达为一个增益矩阵和一个输出映射矩阵, 后者反映了未知输入与输出估计误差之间的内在联系. 最后, 通过数值例子证明了本文方法的有效性.     

基于动态补偿的线性系统最优干扰抑制

本文针对受外部干扰的线性时不变系统研究了基于动态补偿的最优干扰抑制问题,其中干扰信号为已知动态特性的扰动信号.首先,将原系统与扰动系统联立构成增广系统,进而转化为无扰动的标准线性二次最优问题.其次,给出了经具有适当动态阶的补偿器补偿后的闭环系统渐近稳定并且相关的Lyapunov方程正定对称解存在的条件,进一步给定的二次性能指标可写成一个与该解和闭环系统初值相关的表达式.为了得到系统的最优解,将该Lyapunov方程转化为一个双线性矩阵不等式形式,并给出了相应的路径跟踪算法以求得性能指标最小值以及补偿器参数.最后,通过数值算例说明应用本文方法可以不仅能够最小化线性二次指标,而且能够使得系统的干扰得到抑制.     

Suboptimal anisotropic filtering in a finite horizon

Consideration was given to the problem of robust stochastic filtering in a finite horizon for the linear discrete time-varying system. A random disturbance with inaccurately known probabilistic distribution is fed to the system input. Uncertainty of the input disturbance is defined in the information-theoretical terms by the anisotropy functional of a random vector. The sufficient condition for strict boundedness of the anisotropic norm of linear discrete timevarying system assigned by the threshold value (lemma of real boundedness) was proved in terms of the matrix inequalities. Sufficient conditions for boundedness of the anisotropic norm of two limiting cases of the anisotropy levels of the input disturbance (a = 0 and a → ∞) were established. A sufficient existence condition for the estimator guaranteeing boundedness of the anisotropic norm of the estimation error operator by the given threshold value was formulated and proved. Sufficient existence conditions for the estimators of two limiting cases of the anisotropy levels of input disturbance were obtained. The estimation algorithm relies on the recurrent solution of a system of matrix inequalities.     

Stability of a Riccati equation arising in recursive parameter estimation under lack of excitation

Stability properties of the Riccati equation in a recently suggested antiwindup algorithm for recursive parameter estimation are analyzed. Convergence of the resulting dynamic system is implied by that of a linear time-varying difference matrix equation. By means of converging matrix products theory, the linear mapping associated with the system is shown to be a paracontraction with respect to a certain norm. Therefore, measured in that norm, the solution to the matrix equation will not diverge notwithstanding excitation properties of the data. Thus the purpose of anti-windup is achieved.     

具有参数不确定性和外干扰系统的鲁棒H-状态反馈控制

本文考虑具有参数不确定性和外干扰系统的鲁棒Ｈ∞状态反馈控制问题。这个问题的解只需求解一个代数Ｒｉｃｃａｔｉ方程就可得到其状态反馈阵，且这个状态反馈阵仍保持和ＬＱ最优设计相同的形式。运用这样的状态反馈控制。即能保证具有参数不确定性系统是稳定的，又能达到Ｈ∞最优干扰抑制效果。     

线性连续时变系统的状态和输入混合估计:一种对策方法

The $H_\infty$ hybrid estimation problem for linear continuous time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. Based on the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in\hfill terms\hfill of\hfill solutions\hfill to\hfill a\hfill Riccati\hfill diffe-\\rential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix that reflects the internal relations between the unknown input and output estimation error. Both state and unknown inputs estimation are realized by the proposed estimator. Thus, the results in this paper are also capable of dealing with fault diagnosis problems of linear time-varying systems. At last, a numerical example is provided to illustrate the proposed approach.