Almost strictly total positivity of NUAT B-spline basis

Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometrical approach is proposed to prove the collection matrices of NUAT B-spline basis are almost strictly totally positive. In this paper, knot insertion algorithm combined with coefficient variation of NUAT B-spline function, we put forward an intuitive and geometrical method.     

金融数据时间序列相似性度量的应用研究

从应用角度对时间序列数据挖掘中的关键技术一相似性度量一进行了研究。实现了对时间序列的分段线性表示,并将其用于当前主要的几种时间序列距离度量算法。通过将各距离度量算法用于股票收盘数据分析实验,得出实验数据。通过对实验结果的分析并结合各算法的原理,对各方法的适用情况和执行效率进行了分析及比较。通过分析可知,每种算法有自己的特点及适用情况。对于实际应用,应根据实际需求选择合适的距离度量算法。     

基于模拟退火—遗传算法的非线性密钥序列生成器线性复杂度研究

计算线性等价是研究非线性密钥序列生成器线性复杂度的有效方法。本文先介绍了计算线性等价的模拟退火法,然后使用遗传算法对该算法进行改进,最后使用一组密钥序列生成器对改进后的算法进行性能评估,并将改进后的算法和原算法进行了比较。结果表明改进后的算法能比原算法更有效的找到非线性密钥序列生成器的线性等价。     

Quadruple Difference Expansion-Based Reversible Data Hiding Method for Digital Images

ABSTRACT

Lossless data hiding is a special type of data hiding technique that guarantees not only the secret data but also the ability of cover media to be reconstructed without any distortion. A latest lossless data hiding technique is proposed by Hong Lin Jin's that is based on hiding only one data bit in the spatial domain in gray-level image. However, this method uses double difference expansion to embed bits which results in a small embedding capacity. For this purpose, we propose an improved algorithm with the potential of increasing the payload capacity and maintaining good image quality. The proposed improved algorithm is characterized by two aspects. First, the proposed improved reversible data hiding scheme is enhanced to exhibit data hiding in color palette images. Second, the embedding level is improved by using quadruple difference expansion to guarantee the embedding of 2-bit data into color images. Experiments of the proposed improved method have been conducted over several well-known test images. The results show that the proposed improved method significantly improves the embedding capacity over Hong Lin Jin's scheme by the range of 15–35% for grayscale images and 20–46% for color images while still maintaining the quality of the stego-images.     

Using RC4 and AES Key Schedule to Generate Dynamic S-Box in AES

ABSTRACT

Advanced Encryption Standard (AES) block cipher system is widely used in cryptographic applications. Substitution boxes (S-boxes) are a keystone of modern symmetric cryptosystems which bring nonlinearity to the cryptosystems and strengthen their cryptographic security. The S-box component used in classic AES is fixed and not changeable. If the S-box is generated dynamically, the cryptographic strength of AES cipher system would be increased. In this article, we use RC4 and AES Key Expansion algorithms to generate dynamic S-box for AES. The purpose of the proposed approach is to generate more secure S-boxes. The generated S-box will have better results in security analysis. To examine the security, various tests are applied to the new S-box and the results pass all of them.     

Discrete‐time output feedback for Markov jump systems with uncertain transition probabilities

This article addresses the output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees the norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

Dual approaches to strictly positive real controller synthesis with a performance using linear matrix inequalities

The synthesis of controllers that minimize a performance index subject to a strictly positive real (SPR) constraint is considered. Two controller synthesis methods are presented that are then combined into an iterative algorithm. Each method synthesizes optimal SPR controllers by posing a convex optimization problem where constraints are enforced via linear matrix inequalities. Additionally, each method fixes the controller state‐feedback gain matrix and finds an observer gain matrix such that an upper bound on the closed‐loop ‐norm is minimized and the controller is SPR. The first method retools the standard ‐optimal control problem by using a common Lyapunov matrix variable to satisfy both the criteria and the SPR constraint. The second method overcomes bilinear matrix inequality issues associated with the performance and the SPR constraint by employing a completing the square method and an overbounding technique. Both synthesis methods are used within an iterative scheme to find optimal SPR controllers in a sequential manner. Comparison of our synthesis methods to existing methods in the literature is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability of a class of switched positive linear time‐delay systems

This paper addresses the problem of stability for a class of switched positive linear time‐delay systems. As first attempt, the Lyapunov–Krasovskii functional is extended to the multiple co‐positive type Lyapunov–Krasovskii functional for the stability analysis of the switched positive linear systems with constant time delay. A sufficient stability criterion is proposed for the underlying system under average dwell time switching. Subsequently, the stability result for system under arbitrary switching is presented by reducing multiple co‐positive type Lyapunov–Krasovskii functional to the common co‐positive type Lyapunov–Krasovskii functional. A numerical example is given to show the potential of the proposed techniques. Copyright © 2012 John Wiley & Sons, Ltd.     

Stochastic stability and robust stabilization of semi‐Markov jump linear systems

The semi‐Markov jump linear system (S‐MJLS) is more general than the Markov jump linear system (MJLS) in modeling some practical systems. Unlike the constant transition rates in the MJLS, the transition rates of the S‐MJLS are time varying. This paper focuses on the robust stochastic stability condition and the robust control design problem for the S‐MJLS with norm‐bounded uncertainties. The infinitesimal generator for the constructed Lyapunov function is first derived. Numerically solvable sufficient conditions for the stochastic stability of S‐MJLSs are then established in terms of linear matrix inequalities. To reduce the conservativeness of the stability conditions, we propose to incorporate the upper and lower bounds of the transition rate and meanwhile apply a new partition scheme. The robust state feedback controller is accordingly developed. Simulation studies and comparisons demonstrate the effectiveness and advantages of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L₁‐gain and L_∞‐gain. Robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration. Copyright © 2012 John Wiley & Sons, Ltd.