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Stabilization of discrete nonlinear systems based on control Lyapunov functions

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Journal of Systems Engineering and Electronics 2008年第1期19卷 131-133页

作者： Cai Xiushan Wang Xiaodong Lü Ganyun coll. of mathematics Physics and Information Engineering Zhejiang Normal Univ. Jinhua 321004 P.R. China

The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.

关键词： control Lyapunov functions discrete systems stabilization

Simplified iterative algorithm for OFDM phase noise mitigation

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Journal of Systems Engineering and Electronics 2007年第4期18卷 716-720页

作者： Yang Jianhua Zhao Danfeng Yue Li Zhao Chunhui coll. of information and Communication Engineering Harbin Engineering Univ. Harbin 150001 P. R. China

OFDM has been widely adopted in several communication systems. However, OFDM systems are very sensitive to the phase noise, which causes the CPE （common phase error） and ICI （inter-carrier interference）, and thus degrades the system performance significantly. Based on the IEEE 802.11a standard, a simplified iterative phase noise mitigation algorithm is proposed. The proposed algorithm has very low complexity, and requires no additional pilot information. The simulation result shows that good BER performance can be achieved through several few times of iteration.

关键词： phase noise OFDM systems IEEE 802.11a standard inter-carrier interference

Design of twodimensional digital filters using neural networks

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Journal of Systems Engineering and Electronics 2005年第4期16卷 767-771页

作者： Wang Xiaohua He Yigang Electrical and information Engineering coll. Changsha Univ. of Science & Technology Changsha 410077 P. R. China Electrical and information Engineering coll. Hunan Univ. Changsha 410082 P. R. China

A new approach for the design of two-dimensional （2-D） linear phase FIR digital filters based on a new neural networks algorithm （NNA） is provided. A compact expression for the transfer function of a 2-D linear phase FIR filter is derived based on its frequency response characteristic, and the NNA, based on minimizing the square-error in the frequency-domain, is established according to the compact expression. To illustrate the stability of the NNA, the convergence theorem is presented and proved. Design examples are also given, and the results show that the ripple is considerably small in passband and stopband, and the NNA-based method is of powerful stability and requires quite little amount of computations.

关键词： 2-D linear-phase FIR digital filters neural network convergence theorem stability.

Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR(1) Errors

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Acta mathematicae Applicatae Sinica 2012年第1期28卷 49-62页

作者： Chun-Zheng CAO Jin-Guan LIN college of math&Physics Nanjing University of Information Science&TechnologyNanjing 210044China Department of mathematics Southeast UniversityNanjing 210096China

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR（1） errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-S, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-squave and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.

关键词： autocorrelation elliptical distributions heteroscedasticity longitudinal data nonlinear model,score test

THE QUEUE-LENGTH DISTRIBUTION FOR M^x/G/1 QUEUE WITH SINGLE SERVER VACATION

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Acta mathematica Scientia 2000年第3期20卷 397-408页

作者：唐应辉唐小我 Univ Elect Sci & Technol China Coll Management Dept Appl Math Chengdu 610054 Peoples R China

This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.

关键词： server vacation queue length transient distribution equilibrium distribution stochastic decomposition

Global asymptotic stability of a class of nonlinear systems with parametric uncertainty

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Journal of Systems Engineering and Electronics 2009年第1期20卷 168-171页

作者： Cai Xiushan Lu Ganyun Zhang Changjiang He Xiuhui coll. of mathematics Physics and Information Engineering Zhejiang Normal Univ. Jinhua 321004 P. R. China

Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems are deduced. The simulation shows the effectiveness of the method.

关键词： interconnection system Lyapunov functions parametric uncertainty stability.

Asymptotic controllability of a class of discrete-time systems with disturbances

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Journal of Systems Engineering and Electronics 2009年第6期20卷 1296-1300页

作者： Cai Xiushan Wang Xiao Xu Xiuling coll. of mathematics Physics and Information Engineering Zhejiang Normal Univ. Jinhua 321004 P. R. China

This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with *** is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov ***, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop *** addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.

关键词： nonlinear systems asymptotic controllability control Lyapunov functions discrete time disturbances.

The socle of the last term in a minimal injective resolution

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Science China mathematics 2010年第7期53卷 1714-1720页

作者： Huang ZhaoYong Wang Yao Nanjing Univ Dept Math Nanjing 210093 Peoples R China Nanjing Univ Informat Sci & Technol Coll Math & Phys Nanjing 210044 Peoples R China

Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k - 2)-Gorenstein with the injective dimensions of Λ U and U Γ ... 详细信息

关键词： generalized tilting modules (quasi) k-Gorenstein modules socle minimal injective resolution injective dimension

A weak condition for secant method to solve systems of nonlinear equations

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Applied mathematics(A Journal of Chinese Universities) 2009年第1期24卷 90-96页

作者： LIANG Ke-wei HAN Dan-fu ZHANG Hong ZHU Cheng-yan Dept. of math. Zhejiang Univ. Hangzhou 310027 China Dept. of information Technology Zhejiang Economic & Trade Polytechnic Hangzhou 310018 China

In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided. Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.

关键词： secant method Banach space radius of convergence systems of nonlinear equations complexity