离散区间系统的H ∞ 鲁棒控制

研究离散区间系统的鲁棒稳定性分析和鲁棒控制问题,首先基于Ｒｉｃｃａｔｉ方程方法讨论系统的鲁棒稳定性,得到了检验该类系统鲁棒稳定的新的充分条件,然后给出了离散区间系统鲁棒控制器存在的充分条件,并通过求解修正的代数Ｒｉｃｃａｔｉ方程,给出了该控制器的设计方法。     

离散代数Riccati方程解的上下界研究

研究离散时间代数Ｒｉｃｃａｔｉ方程（ＤＡＲＥ）给了了ＤＡＲＥ解的上界和下界估计人公式，所得结果与现有结果比较，具有较小的保守性，计算实例表明本方法的有效性。     

Wiener滤波新方法

基于ＡＲＭＡ新息模型提出Ｗｉｅｎｅｒ滤波的一种新的时域方法。对带状态空间模型的线性离散随机系统，提出一种Ｗｉｅｎｅｒ状态估计器，可统一处理最优滤波、平滑和预报问题，且具有渐近稳定性，避免了求解Ｄｉｏｐｈａｎｔｉｎｅ方程和Ｒｉｃｃａｔｉ方程。仿真例子说明了其有效性。     

基于矩阵符号函数求解代数Riccati方程的ANN方法

本文基于矩阵符号函数方法，运用神经网络技术的智能特性，给出了一种求解连续及离散代数Ｒｉｃｃａｔｉ方程的ＡＮＮ方法，最后给出这种方法的应用例子，验证了该方法的有效性及可靠性。     

离散双自由度鲁棒设计H∞方法研究*

以离散Ｈ∞全信息问题为基础，给出并证明了离散系统一类扰动前馈问题的设计方法，得到了控制器的参数化描述，在此基础上，研究了离散双自由度设计的Ｈ∞方法，在这一类问题中，相应标准离散Ｈ∞设计中的第二个离散代数Ｒｉｃｃａｔｉ方程不再需要求解，最后对精馏塔系统进行设计，得到了满意的结果。     

δ算子的LQR设计

证明了在相同指标要求下δ离散域的反馈控制应完全等同于Ｚ域的反馈控制，导出了δ域二次型最优解，证明了在相同加权下当采样周期Ｔ→时，δ域的最优增益趋近于连续域最优解，从而可以通过解连续域的Ｒｉｃｃａｔｉ方程直接得到离散控制律，δ域的闭环特性比Ｚ域更接近连续域的闭环特性，并对几种方法进行了比较研究，验证了上述结论。     

矩阵代数Riccati方程的进一步研究

研究矩阵代数Ｒｉｃｃａｔｉ方程ＰＡ＋Ａ‘Ｐ＋Ｃ’ＰＣ－（ＰＢ＋Ｃ‘ＰＤ）（Ｒ＋Ｄ’ＰＤ）＋Ｑ＝０,所得结果改进了文献（７）的结论。     

线性离散不确定系统区域极点配置的状态反馈实现方法

研究利用状态反馈对线性离散不确定系统进行区域极点配置的问题。导出了一个由离散代数Ｒｉｃａｔｉ方程表示的对线性离散不确定系统进行区域极点配置的充分条件,并给出了一个通过求解该方程来确定状态反馈增益矩阵的算法。     

线线离散不确定系统区域极点配置的状态反馈实现方法

研究利用状态反馈对线性离散不确定系统进行区域极点配置的问题。导出了一个由离散代数Ｒｉｃｃａｔｉ方程表示的对线性离散不确定系统进行区域极点配置的充分条件,并给出了一个通过求解该方法来确定状态反馈增益矩阵的算法。     

Systolic算洁和结构求解代数Riccati方程

本文基于矩阵的符号函数法，提出了一种Ｕ－Ｄ分解算法和脉动（Ｓｙｓｔｏｌｉｃ）结构有效地求解代数Ｒｉｃｃａｔｉ方程以及用固定大小的方形阵列解决大型问题的方法．     

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.     

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.     

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.     

On upper bounds for the unified algebraic Riccati equation

In recent years, several eigenvalues, norms and determinants bounds have been investigated separately for the solutions of continuous and discrete Riccati equations. In this paper, an upper bound for solution of the unified Riccati equation is presented. In the limiting cases, the result reduces to a new upper bound for the solution of continuous and discrete Riccati equation.     

基于Delta算子的统一代数Lyapunov方程解的上下界

基于Delta算子描述,统一研究了连续代数Lyapunov方程(CALE)和离散代数Lyapunov方程(DALE)的定界估计问题.采用矩阵不等式方法,给出了统一的代数Lyapunov方程(UALE)解矩阵的上下界估计,在极限情形下可分别得到CALE和DALE的估计结果.计算实例表明了本文方法的有效性.     

Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations

In this paper, we propose upper bounds for the sum of the maximal eigenvalues of the solutions of the continuous coupled algebraic Riccati equation (CCARE) and the discrete coupled algebraic Riccati equation (DCARE), which are then used to infer upper bounds for the maximal eigenvalues of the solutions of each Riccati equation. By utilizing the upper bounds for the maximal eigenvalues of each equation, we then derive upper matrix bounds for the solutions of the CCARE and DCARE. Following the development of each bound, an iterative algorithm is proposed which can be used to derive tighter upper matrix bounds. Finally, we give numerical examples to demonstrate the effectiveness of the proposed results, making comparisons with existing results.     

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.     

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.     

Upper matrix bounds for the discrete algebraic Riccati matrixequation

We propose upper matrix bounds for the discrete algebraic Riccati matrix equation. We show that our results are less restrictive than the previous bounds. Finally, we give numerical examples in order to verify the effectiveness of our results     

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