Hilbert-Schmidt-Hankel norm model reduction for matrix second-order linear systems

This paper considers the optimal model reduction problem of matrix second-order linear systems in the sense of Hilbert-Schmidt-Hankel norm, with the reduced order systems preserving the structure of the original systems. The expressions of the error function and its gradient are derived. Two numerical examples are given to illustrate the presented model reduction technique.     

Robust H∞ control of norm bounded uncertain systems via Markovian approach

This paper presents a new approach to analyze and synthesize linear uncertain systems with time‐varying norm bounded uncertainty. Firstly, the uncertainty set is classified into several different subsets according to the maximum singular value of uncertainty. Then, based on the proposed classification, the original uncertain system is transformed into a Markovian jump system. By an uncertainty‐dependent Lyapunov function, new version of bounded real lemma is developed and two sufficient conditions for designing uncertainty‐dependent controllers are established. Finally, numerical examples and simulations are used to demonstrate the utility of the given methods. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一种鲁棒稀疏表示的单样本人脸识别算法

稀疏表示在人脸识别问题上取得了非常优秀的识别结果,但在单样本条件下,算法性能下降严重。为提高单样本条件下稀疏表示的应用能力,提出一种鲁棒稀疏表示单样本人脸识别算法(RSR)。通过使用每张人脸图像创建一组位置图像,扩充每个对象训练样本,并利用L2,1范数约束,保证RSR选择正确对象的位置图像。在AR和Extended Yale B人脸数据库上进行评测,实验结果表明RSR能够有效处理存在遮挡或光照变化的人脸图像,获得了较好的单样本人脸识别准确率,具有很强的鲁棒性。     

光滑lp范数压缩感知图像重构优化算法

针对已有压缩感知重构算法重构精度不高、消耗时间长的问题,在研究[lp]范数和光滑[l0]范数压缩感知重构算法的基础上提出改进算法。通过极大熵函数构造一种光滑函数来逼近最小[lp] 范数,对解序列进行离散化来近似最小[lp]范数的最优解,结合图像分块压缩感知技术（BCS）,在MATLAB中对测试图像进行仿真实验。结果表明,与传统的BOMP（Block Orthogonal Matching Pursuit）算法和IRLS（Iteratively Reweighted Least Squares）算法相比,改进后的算法不仅提高了重构精度,而且大大降低运行时间。     

Internal positivity preserved model reduction

This article studies model reduction of continuous-time stable positive linear systems under the Hankel norm, H _∞ norm and H ₂ norm performance. The reduced-order systems preserve the stability as well as the positivity of the original systems. This is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the Lyapunov matrices are decoupled with the system matrices. In this way, the positivity constraints in the reduced-order model can be imposed in a natural way. As the model reduction performances are expressed in linear matrix inequalities with equality constraints, the desired reduced-order positive models can be obtained by using the cone complementarity linearisation iterative algorithm. A numerical example is presented to illustrate the effectiveness of the given methods.     

A structure-preserving algorithm for the minimum H ∞ norm computation of finite-time state feedback control problem

The algorithm being developed here is based on the generating function approach for finite-time H _∞ control and application of canonical transformation of linear Hamiltonian system. First, an equivalent finite-time H _∞ control law in terms of the third-type generating function is derived. Then, by using symplectic structure of the Hamiltonian system's state transition matrix, a group of matrix recursive formulae are deduced for the evaluation of the finite-time H _∞ control law. Combining with a matrix singularity testing procedure, this recursive algorithm verifies the existence condition of sub-optimal H _∞ controllers and gives the minimum H _∞ norm of finite-time control systems. Inherited from the canonical transformation, the matrix recursive formulae have a standard symplectic form; this structure-preserving property helps facilitate reliable and effective computation. Numerical results show the effectiveness of the proposed algorithm.     

Signal-to-noise ratio fundamental constraints in discrete-time linear output feedback control

In the present paper we study the fundamental limitations on stability that arise when an additive coloured Gaussian noise (ACGN) channel is explicitly considered in a linear time invariant (LTI) control feedback loop. By considering a linear setting we can express the fundamental limitation on stability as a lower bound in closed-form on the ACGN channel signal-to-noise ratio (SNR). Outside the context of networked control, the obtained lower bound can be interpreted as an H₂ performance limitation.     

On a class of positive linear differential equations with infinite delay

We give an explicit criterion for positivity of the solution semigroup of linear differential equations with infinite delay and a Perron-Frobenius type theorem for positive equations. Furthermore, a novel criterion for the exponential asymptotic stability of positive equations is presented. Finally, we provide a sufficient condition for the exponential asymptotic stability of positive equations subjected to structured perturbations. A simple example is given to illustrate the obtained results.     

Abelian complexity of infinite words associated with quadratic Parry numbers

We derive an explicit formula for the Abelian complexity of infinite words associated with quadratic Parry numbers.     

基于2DPCA和压缩感知的人脸识别方法

提出一种基于二维主成份分析(2DPCA)和压缩感知的人脸识别方法.阐述2DPCA提取特征向量的工作原理,利用压缩感知方法求解待识别图像在足够样本下的稀疏表示.由所有训练图的特征向量构成测量矩阵,将每一幅待识别图像的特征向量作为测量值,由压缩感知中求解的L1范数极小值得到待识别图像的编码信号,根据该编码信号识别人脸图像....