A detailed comparative analysis of all practical algorithms to compute lower bounds on the structured singular value

μ analysis is one of the most efficient techniques to evaluate the stability margins and the performance levels of linear time-invariant systems in the presence of structured time-invariant uncertainties. The exact computation of the structured singular value μ is known to be NP hard in the general case, but several methods have been developed in the last 30 years to compute accurate and reliable bounds. In this paper, all existing μ lower bound algorithms are reviewed and the most relevant ones are evaluated on a wide set of real-world benchmarks, corresponding to various fields of application, system dimensions and structures of the uncertainties. The results are thoroughly analyzed and simple improvements to the existing algorithms are proposed to approach the exact value of μ with a reasonable computation cost. Conclusions show that non-conservative values can be obtained in almost all cases. A brief extension to skew-μ analysis confirms the good results obtained in the classical μ case.     

Robustness of the stability of feedback systems with respect to small time delays

It is shown that a feedback system is robustly stable with respect to small time delays if and only if it is stable for zero time delay and a structured singular value is less than one.     

Analysis of robust performance with multiple objectives

Performance robustness with multiple objectives of linear control systems having structured norm-bounded uncertainty is considered. In order to deal with any two objective functions Ψ₁ and Ψ₂ associated with a single feedback control system, the combined criterion Ψ[Ψ₁ ψ₂]Ψ S 1 is often used. The paper, however, considers Ψ ψ₁ Ψ 1 and Ψ W, 11 1 directly. It is shown that it is possible to assess robust performance of two objectives by a single μ test if repeated nonscalar blocks are adequately introduced in the structure of μ. In other words, a performance robustness problem with multiple objectives is proved to be equivalent to a stability robustness problem with extra repeated uncertainty blocks. This equivalence theorem is applicable to various system and norm setups including sampled-data systems.     

关于结构奇异值的一个注记

１引言Ｄｏｙｌｅ在１９８２年提出的结构奇异值（μ）方法是分析和综合结构式不确定系统的有力工具［１,２］．基于结构奇异值分析的小μ定理［２］给出了具有多个摄动块的线性动态系统鲁棒稳定的充要条件．而鲁棒性能定理［２］则进一步地将鲁棒稳定性问题和鲁棒性能问题统一成μ分析问题．然而．我们注意到,在所有研究结构奇异值的文献中,均要求块对角摄动矩阵中每个子摄动块是方的．这一要求无疑大大限制了μ方法的应用,因为非方摄动块在系统中是经常存在的．此时对Ｄｏｙｌｅ给出的结构奇异值的上界函数［１］必须进行修正．２非方…     

多变量过程的鲁棒解耦

运用Doyle的结构奇异值理论,提出了不确定系统解耦控制器设计方法.该方法在保证闭环系统稳定性和动态性能前提下,使解耦控制器对范数约束的不确定系统作最大限度地解耦.仿真表明,这种鲁棒解耦控制器效果良好.     

Computation of the robustness margin with the skewed μ tool

Methods for the direct computation of the maximal structured singular value (s.s.v.) over the frequency range require a recursive application of μ analysis. Introducing the v measure as a skewed s.s.v., we point out the problem can be solved by a single application of the v tool. A mixed v upper bound is then proposed, which provides a direct solution to the problem. The relationship between the mixed μ and v upper bounds is moreover clarified. The nonnegativity of the sensitivity of the mixed μ upper bound is finally obtained as a corollary.     

固定阶数的结构奇异值反馈控制器的设计

１引言目前常用的结构奇异值综合算法仍是Ｄ－Ｋ交替寻优算法［２］和μ－Ｋ交替寻优算法［３］,但这两种算法计算繁复,得到的控制器阶数也较高,造成数值计算上的困难,使结构奇异值理论难以为工程应用所接受．因此,研究便于工程应用的μ综合方法是μ理论的一个重要课...     

Computation of the robustness margin with the skewed μ tool

Methods for the direct computation of the maximal structured singular value (s.s.v.) over the frequency range require a recursive application of μ analysis. Introducing the v measure as a skewed s.s.v., we point out the problem can be solved by a single application of the v tool. A mixed v upper bound is then proposed, which provides a direct solution to the problem. The relationship between the mixed μ and v upper bounds is moreover clarified. The nonnegativity of the sensitivity of the mixed μ upper bound is finally obtained as a corollary.     

基于LMI的μ方法及其在电力系统中的应用

提出了一个新的基于linear matrix inequality(LMI)的混合结构奇异值(μ)分析与综合方法,通过采用S-过程,将Robust LMI形式的判据简化,得到了可验证的基于LMI的μ分析综合判据.该判据是基于状态空间描述的,从而消除了频率扫描过程和频率响应曲线拟合过程并具有更好的数值性态.将该方法应用于典型电力系统励磁控制的鲁棒稳定性分析和鲁棒控制器的设计中,数值仿真结果同现有AVR+PSS控制器的结果所做比较表明该方法的有效性.     

Lyapunov functions for the multivariable Popov criterion with indefinite multipliers

We demonstrate the existence of Lur’e-Postnikov type Lyapunov functions for a reasonably general form of the multivariable Popov criterion. In particular, the multipliers need not be positive semi-definite. We discuss the application to the special cases where the feedback element is either diagonal, unstructured or linear.     

复结构奇异值的几何解释及其计算:两块情形

应用几何方法给出两块情形复结构奇异值的几何解释,并提出一种简单迭代计算方法.该方法求的是结构奇异值的真值而非其某一上界或下界.     

On robust performance in

In this paper we consider the robust performance problem in with scalar perturbations. We illustrate how the worst case performance can be regarded as an norm of a function of several complex variables. Based on this characterization we show how the worst case performance can be obtained from the norm of a single system. This system is constructed from the original nominal system with the perturbations replaced by certain all-pass functions. We show that as the order of the all-pass functions goes to infinity, this norm converges to the worst case performance. The implications of this characterization for computing the complex structured singular value and robust synthesis are discussed, though at present, this method does not seem to provide an efficient algorithm for this computation.     

面向矩阵秩函数准确估计的自表示子空间聚类方法

传统子空间聚类方法通常使用矩阵核范数代替矩阵秩函数进行低秩矩阵恢复,然而在目标优化过程中主要关注低秩矩阵大奇异值的影响,容易导致矩阵秩估计不准确的问题。为此,在分析矩阵奇异值长尾分布特点基础上,提出使用基于截断Schatten-p范数的低秩子空间聚类模型。该模型充分考虑小奇异值对低秩矩阵恢复过程的贡献,利用小奇异值信息拟合矩阵奇异值的长尾分布,通过对矩阵秩函数进行准确估计以提升子空间聚类性能。实验结果表明,与现有加权核范数子空间聚类WNNM-LRR和近邻约束子空间聚类BDR算法相比,在Extended Yale B数据集上的聚类准确性分别提升了11%和8%,所提方法能够更好地拟合数据奇异值分布以及生成准确的相似度矩阵。     

Synchronization of diffusively-coupled limit cycle oscillators

We develop analytical and numerical conditions to determine whether limit cycle oscillations synchronize in diffusively coupled systems. We examine two classes of systems: reaction–diffusion PDEs with Neumann boundary conditions, and compartmental ODEs, where compartments are interconnected through diffusion terms with adjacent compartments. In both cases the uncoupled dynamics are governed by a nonlinear system that admits an asymptotically stable limit cycle. We provide two-time scale averaging methods for certifying stability of spatially homogeneous time-periodic trajectories in the presence of sufficiently small or large diffusion and develop methods using the structured singular value for the case of intermediate diffusion. We highlight cases where diffusion stabilizes or destabilizes such trajectories.     

Bounds on generalized structured singular values via the Perron root of matrix majorants

The purpose of this paper is to present several bounds upon the structured singular value. We first adopt a generalized notion of the structured singular value which is useful for problems where uncertainties are assumed to be bounded in an l_p-induced matrix norm. Two different type of bounds, in terms of Perron root and interaction parameters respectively, are given for the new structured singular value and their relations are discussed. These bounds are useful in that they are easy to compute and may be further analyzed to provide insights useful in design.     

基于SURF特征的多功能彩色图像水印算法（CIDE2013推荐）

针对目前大多数水印算法功能较单一,提出了一种可以同时进行版权保护和内容认证的多功能彩色图像双水印算法。首先,将原始图像由RGB空间转换到YUV空间,提取亮度分量的SURF特征点,根据特征点的主方向构造描述向量并将其拆分为两个子向量,分别计算它们与一个参考向量之间的余弦夹角,通过比较夹角的大小关系来构造鲁棒零水印序列;然后对原始图像进行 分块,对子图像块奇异值范数进行异或运算来产生脆弱水印信息,并将其嵌入至图像空域的最低有效位。版权归属鉴定时通过计算原始鲁棒零水印序列和从待检测图像中提取的水印序列之间的BCR相关系数作为鉴定的依据,内容认证时通过比较图像最低有效位和脆弱水印信息是否一致来实现篡改的检测和定位。实验结果表明,本文提出的算法具有良好的透明性和较高的计算效率,同时具备版权保护和内容认证的双重功能。     

基于稀疏表示的信号DOA估计

将信号DOA的估计问题转换为一个联合稀疏表示的求解问题.通过对接收数据矩阵的奇异值分解实现各时间和频率快拍数据的联合;然后通过求解一个平滑l0范数稀疏约束的联合优化问题实现信号源DOA的估计.基于稀疏表示的信号DOA估计方法不仅能够有效地减少数据量,而且具有以下优点:更好的抗噪声性能、更高的计算效率、适用于相关和非相关信号.通过与其他DOA估计方法的比较,表明了该方法的有效性和优越性.