2006年, 第19卷, 第2期　刊出日期：2006-06-20

  

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  Stability of N-Dimensional Linear Systems with Multiple Delays and Application to Synchronization

  Weihua Deng;Jinhu Lü;Changpin Li

  Journal of Systems Science and Complexity. 2006, 19(2): 149-156. https://doi.org/10.1007/s1

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  This paper further investigates the stability of the n-dimensional linear systems with multiple delays. Using Laplace transform, we introduce a definition of characteristic equation for the n-dimensional linear systems with multiple delays. Moreover, one sufficient condition is attained for the Lyapunov globally asymptotical stability of the general multi-delay linear systems. In particular, our result shows that some uncommensurate linear delays systems have the similar stability criterion as that of the commensurate linear delays systems. This result also generalizes that of Chen and Moore (2002). Finally, this theorem is applied to chaos synchronization of the multi-delay coupled Chua’s systems.
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  Design Methodology of Networked Software Evolution Growth Based on Software Patterns

  Keqing He;Rong Peng;Jing Liu;Fei He;Peng Liang;Bing Li

  Journal of Systems Science and Complexity. 2006, 19(2): 157-181. https://doi.org/10.1007/s1

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  Recently, some new characteristics of complex networks attract the attentions of scientists in different fields, and lead to many kinds of emerging research directions. So far, most of the research work has been limited in discovery of complex network characteristics by structure analysis in large-scale software systems. This paper presents the theoretical basis, design method, algorithms and experiment results of the research. It firstly emphasizes the significance of design method of evolution growth for network topology of Object Oriented (OO) software systems, and argues that the selection and modulation of network models with various topology characteristics will bring un-ignorable effect on the process of design and implementation of OO software systems. Then we analyze the similar discipline of “negation of negation and compromise” between the evolution of network models with different topology characteristics and the development of software modelling methods. According to the analysis of the growth features of software patterns, we propose an object-oriented software network evolution growth method and its algorithms in succession. In addition, we also propose the parameter systems for OO software system metrics based on complex network theory. Based on these parameter systems, it can analyze the features of various nodes, links and local-world, modulate the network topology and guide the software metrics. All these can be helpful to the detailed design, implementation and performance analysis. Finally, we focus on the application of the evolution algorithms and demonstrate it by a case study. Comparing the results from our early experiments with methodologies in empirical software engineering, we believe that the proposed software engineering design method is a computational software engineering approach based on complex network theory. We argue that this method should be greatly beneficial for the design, implementation, modulation and metrics of functionality, structure and performance in large-scale OO software complex system.
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  Testing for Long Memory in the Asian Foreign Exchange Rates

  Abdol S. Soofi;Shouyang Wang;Yuqin Zhang

  Journal of Systems Science and Complexity. 2006, 19(2): 182-190. https://doi.org/10.1007/s1

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  In this paper, we use the plug-in and Whittle methods that are based on spectral regression analysis to test for the long memory property in 12 Asian/dollar daily exchange rates. The results according to the plug-in method show that with the exception of Chinese renminbi all series may have long memory properties. The results based on the Whittle method, on the other hand, show that only Japanese yen and Malaysian ringgit may have long memory properties. It is well known that inference about the differencing parameter, d, in presence of structural break in a series entails considerable difficulties. Therefore, given the financial crisis of 1997–1998 in Asia, further tests for unravelling of the memory property and presence of structural break in the exchange rate series are required.
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  Analysis and Computational Algorithm for Queues with State-Dependent Vacations II: M(n)/G/1/K

  Xiuli Chao;Ayyar Rahman

  Journal of Systems Science and Complexity. 2006, 19(2): 191-210. https://doi.org/10.1007/s1

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  We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M(n)/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O(K3).
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  Extended Casimir Approach to Controlled Hamiltonian Systems

  Yuqian Guo;Daizhan Cheng

  Journal of Systems Science and Complexity. 2006, 19(2): 211-218. https://doi.org/10.1007/s1

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  In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the H∞ control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.
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  Solution Classification for the Nonperspective-Three-Point Problem

  Jianliang Tang;Wensheng Chen

  Journal of Systems Science and Complexity. 2006, 19(2): 219-226. https://doi.org/10.1007/s1

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  In the PnP problem, the imaging devices follow the perspective rule and the imaging rays pass through a common point. However, there are many new imaging devices being developed for robot navigation or other fields with the advance in imaging technologies for machine vision. These devise are not necessarily being designed to follow the perspective rule in order to satisfy some design criterion and, thus, the imaging rays may not pass through a common point. Such generalized imaging devices may not be perspective and, therefore, their poses cannot be estimated with traditional perspective technique. Using the Wu-Ritt’s zero decomposition method, the main component for the nonperspective-three-point problem is given. We prove that there are at most eight solutions in the general case and give the solution classification for the NP3P problem.
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  Matter-Element Modeling of Parallel Structure and Application about Extension PID Control System

  Rongde Lu;Zonghai Chen

  Journal of Systems Science and Complexity. 2006, 19(2): 227-235. https://doi.org/10.1007/s1

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  This article describes in detail a new method via the extension predictable algorithm of the matter-element model of parallel structure tuning the parameters of the extension PID controller. In comparison with fuzzy and extension PID controllers, the proposed extension PID predictable controller shows higher control gains when system states are away from equilibrium, and retains a lower profile of control signals at the same time. Consequently, better control performance is achieved. Through the proposed tuning formula, the weighting factors of an extension-logic predictable controller can be systematically selected according to the control plant. An experimental example through industrial field data and site engineers’ experience demonstrates the superior performance of the proposed controller over the fuzzy controller.
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  Quadratic Admissible Estimate of Covariance in Pseudo-Elliptical Contoured Distribution

  Hengjian Cui;Xiuhong Gao

  Journal of Systems Science and Complexity. 2006, 19(2): 236-255. https://doi.org/10.1007/s1

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  This article mainly discusses the admissibility of quadratic estimate of covariance in pseudo-elliptical distribution. Under the quadratic loss function, the necessary and sufficient conditions that a quadratic estimator is an admissible estimator of covariance in the class of quadratic estimators are obtained. A complete class of the quadratic estimator class is also given.
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  Implicitization of Partial Differential Rational Parametric Equations

  Guangwei Li

  Journal of Systems Science and Complexity. 2006, 19(2): 256-265. https://doi.org/10.1007/s1

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  In this paper, we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P. (1)To find a characteristic set for the implicit prime ideal of P; (2) To find a canonical representation for the image of P; (3)To decide whether the parameters of P are independent, and if not, to re-parameterize P so that the new parametric equations have independent parameters; (4) To compute the inversion maps of P, and as a consequence, to decide whether P is proper.
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  A Simple Method for Constructing Orthogonal Arrays By the Kronecker Sum

  Yingshan Zhang;Weiguo Li;Shisong Mao;Zhongguo Zheng

  Journal of Systems Science and Complexity. 2006, 19(2): 266-273. https://doi.org/10.1007/s1

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  In this article, we propose a new general approach to constructing asymmetrical orthogonal arrays, namely the Kronecker sum. It is interesting since a lot of new mixed-level orthogonal arrays can be obtained by this method.
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  Output Feedback Control for Mimo Nonlinear Systems with Exogenous Signals

  Ying Zhou;Yuqiang Wu

  Journal of Systems Science and Complexity. 2006, 19(2): 274-287. https://doi.org/10.1007/s1

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  The paper addresses the global output tracking of a class of multi-input multi-output (MIMO) nonlinear systems affected by disturbances, which are generated by a known exosystem. An adaptive controller is designed based on the proposed observer and the backstepping approach to asymptotically track arbitrary reference signal and to guarantee the boundedness of all the signals in the closed loop system. Finally, the numerical simulation results illustrate the effectiveness of the proposed scheme.
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  Convergence Properties of the Dependent PRP Conjugate Gradient Methods

  Shujun Lian;Changyu Wang;Lixia Cao

  Journal of Systems Science and Complexity. 2006, 19(2): 288-296. https://doi.org/10.1007/s1

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  In this paper, a new region of βk with respect to βkPRP is given. With two Armijo-type line searches, the authors investigate the global convergence properties of the dependent PRP conjugate gradient methods, which extend the global convergence results of PRP conjugate gradient method proved by Grippo and Lucidi (1997) and Dai and Yuan (2002).