New coprimeness over multivariable polynomial matrices and its application to control delay systems

This paper presents a new notion of coprimeness over multivariable polynomial matrices, where a single variable is given priority over the remaining variables. From a characterization through a set of common zeros of the minors, it is clarified that the presented coprimeness is equivalent to weakly zero coprimeness in the particular variable. An application of the presented coprimeness to control systems with non-commensurate delays and finite spectrum assignment is also presented. Because the presented coprimeness is stronger than minor coprimeness, non-commensurate delays are difficult to deal with in algebraic control theory. The “rational ratio condition” between delays, which can reduce non-commensurate delays to commensurate delays, proves to be both powerful and practical concept in algebraic control theory for delay systems.     

三对角对称矩阵逆特征问题

In this paper, four inverse eigenproblems with giventhree eigenvalues and corresponding eigenvectors are considered, somenecessary and sufficient conditions under which there exists a uniquesolution for these problems are given. Furthermore some numerical algorithmsand some numerical experiments are given.     

Re-engineering of the design process for concurrent engineering

According to the requirements of concurrent engineering, three interdependency relationships (uncoupled relationship, coupled relationship and decoupled relationship) between design activities are presented in this paper. And the coupled relationship plays an important role in concurrent product design process. To represent the precedence relationships among design activities, a directed graph is used to describe the design process. And the interdependency relationship between activities is illustrated by a Design Structure Matrix which is the transpose of the accessibility matrix of the corresponding graph. Using the DSM, an algorithm of recognizing the coupled activities during the design process is presented. Moreover, an algorithm to figure out the order levels of activities during the design process is proposed. And both algorithms are illustrated with a die design example.     

Research and Implementation of Task Management Model in Product Development Process Management

The implementation of product development process management (PDPM) is an effective means of developing products with higher quality in shorter lead time. It is argued in this paper that product, data, person and activity are basic factors in PDPM With detailed analysis of these basic factors and their relations in product developmed process, all product development activities are considered as tasks and the management of product development process is regarded as the management of task execution A task decomposition based product development model is proposed with methods of constructing task relation matrix from layer model and constraint model resulted from task decomposition. An algorithm for constructing directed task graph is given and is used in the management of tasks. Finally, the usage and limitation of the proposed PDPM model is given with further work proposed.     

Source number estimation and separation algorithms of underdetermined blind separation

Recently, sparse component analysis （SCA） has become a hot spot in BSS research. Instead of independent component analysis （ICA）, SCA can be used to solve underdetermined mixture efficiently. Two-step approach （TSA） is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However, the estimation of the source number is an obstacle. In this paper, a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that, the sources are recovered by the shortest path method （SPM）. Simulations show the availability and robustness of the proposed method.     

Stability analysis of networked control systems with time-varying sampling periods

In this paper, we present an interval model of networked control systems with time-varying sampling periods and time-varying network-induced delays and discuss the problem of stability of networked control systems using Lyapunov stability theory. A sufficient stability condition is obtained by solving a set of linear matrix inequalities. In the end, the illustrative example demonstrates the correctness and effectiveness of the proposed approach.     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.     

基于F2上遍历矩阵的Shamir三次传递协议的实现

给出了Shamir三次传递协议的一种新的实现方案.与已有的基于离散对数问题的实现方案不同,它是基于在特定的非交换壹半群(m,·)中,由A和B＝x·A·y求解x和y的难度;为此我们选取有限域F2上的n×n矩阵在F2矩阵乘法下所构成的非交换壹半群作为研究的对象,利用F2上"遍历矩阵"的密码学特性,提出了一个基于F2上遍历矩阵的Shamir三次传递协议的实现方案,并对可能的攻击手段进行了分析.为了增加通讯的安全性,提出了"强壮矩阵"的概念,并对于给定的两个遍历矩阵Q1和Q2,给出了关于Q1,Q2的强壮矩阵的判别标准和寻找算法;利用<Q1>,<Q2>以及关于Q1,Q2的强壮矩阵m,可以构造一个单向(陷门)函数,基于该单向函数,可具体实现Shamir三次传递协议、Diffie-Hellman密钥交换协议以及常规的公钥密码.     

An LMI approach to constrained optimization with homogeneous forms

This paper considers the problem of determining the minimum Euclidean distance of a point from a polynomial surface in . It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent linear matrix inequality (LMI) techniques can be exploited for solving this problem. The first result of the paper shows that a lower bound to the global minimum can be achieved via the solution of a one-parameter family of linear matrix inequalities (LMIs). It is also pointed out that for some classes of problems the solution of a single LMI problem provides the lower bound. The second result concerns the tightness of the bound. It is shown that optimality of the lower bound amounts to solving a system of linear equations. An application example is finally presented to show the features of the approach.