关于多维移变离散系统的输入输出稳定性

本文的反例证明：论文「１」中关于多维移变离散系统的输入输出稳定性的定量不是多维移变离散系统稳定性的充分必要条件，本文提出了对该定理的两个修正：定理ｌａ与定理ｌｂ，如定理ｌａ和定理ｌｂ所指出的，对于一般多维多变离菜系统的输入输出稳定性。     

二维离散赫维茨多项式的复系数列表检验法

本文提出了新的二维离散赫维茨（Ｈｕｒｗｉｔｚ）多项式的检验定理，与现有的二维离散赫维茨多项式的代数检验法不同，本文方法是直接对复变量系数列表，然后利用我们提出的检验定理进行零点存在性检验，不需在整个Ｘ∈（－１，１）的实数域逐点检验，并且无有理多项式出现，因而检验过程大为简化，计算量大为减少，只须进行有限次运算，即可确定其是否是二维离散赫维茨多项式。     

二维离散赫维茨多项式的复系数列表检验法

本文提出了新的二维离散赫维茨(Hurwitz)多项式的检验定理。与现有的二维离散赫维茨多项式的代数检验法不同,本文方法是直接对复变量系数列表,然后利用我们提出的检验定理进行零点存在性检验,不需在整个x|-1,1]的实数域进行逐点检验,并且无有理多项式出现。因而检验过程大为简化,计算量大为减少,只须进行有限次运算,即可确定其是否是二维离散赫维茨多项式。     

多胞型二维多项式的Schur稳定性

本文提出多胞型二维多项式的Schur稳定的充分必要条件。我们揭示多胞型二维多项式的系数具有线性仿射特性。基于这一仿射特性,将多胞型二维多项式视为具有复变系数的多胞型一维多项式,我们证明多胞型二维多项式的稳定性可由其有限的棱边多项式的稳定性保证。我们提供了一种棱边多项式的稳定性检验算法。     

二维数字滤波理论的进展

本文对近年来在二维数字滤波理论方面的进展作了综述,介绍了二维非递归数字滤波器和二维递归数字滤波器,分别讨论了它们的设计和实现,并介绍了几种检验二维递归滤波器稳定性的方法。最后一节简介二维卡尔曼滤波器,指出了它在实现上存在的问题。     

区间矩阵的Hurwitz与Schur鲁棒稳定性检验

提出基于二维面检验的区间矩阵Ｈｕｒｗｉｔｚ与Ｓｃｈｕｒ鲁棒稳定的充分必要条件。证明区间矩阵的Ｈｕｒｗｉｔｚ与Ｓｃｈｕｒ鲁棒稳定性可由其二维表面的稳定性保证。为证明本文区间矩阵的鲁棒稳定性检验的可应用性，给出了实例。     

八维广义同步系统在伪随机数发生器中的应用

该文提出一类4维离散系统。利用系统平衡点处 Jacobi 矩阵的特征值来分析系统在平衡点处的稳定性,建立了一个判别这类系统为周期或混沌的定理。依据该定理构造了一个新的4维离散系统。该系统具有正的Lyapunov指数,数值模拟显示该系统的动力学行为具有混沌特性。结合该系统和系统广义同步定理构造了一个8维广义同步混沌系统。利用该系统构造了一个16 bit混沌伪随机数发生器 (CPRNG),其密钥空间大于21245。利用FIPS 140-2 检测/广义FIPS 140-2检测判别标准分别检测由CPRNG, Narendra RBG, RC4 PRNG和ZUC PRNG生成的1000个长度为20000 bit的密钥流的随机性。检测结果表明,分别有100%/99%, 100%/82.9%, 99.9%/ 98.8%和100%/97.9%密钥流通过FIPS 140-2检测/广义FIPS 140-2 检测标准。数值仿真显示不同密钥流之间有平均50.004%不同码。结果说明设计的伪随机数发生器有好的随机性,可以抵抗穷尽攻击。该文提出的CPRNG为密码安全的研究与发展提供了新的工具。     

基于神经网络的任意幅频响应二维FIR线性相位数字滤波器的优化设计

本文提出了一种用神经网络算法来设计任意幅频响应二维FIR线性相位数字滤波器的新方法,其主要思想是使频率响应平方误差函数最小化.根据给定的任意幅频响应指标,按该算法可直接获得滤波器系数.为保证该算法的稳定性,提出并证明了该算法的收敛定理.文中给出了滤波器优化设计实例,计算机仿真结果表明由该方法设计的任意幅频响应二维数字滤波器波动小,算法收敛速度快,稳定性强.     

关于二维数字滤波器稳定性的检验

二维数字滤波器简单的稳定性检验的开发,仍是一个重要的研究领域。在这方面,本文报告了关于修正的安德森(Anderson)和朱里(July)检验法的一些结果。本文还介绍一种以变置转换为基础的另一种稳定性检验方法,并给出了说明所提出的算法的几个实例。     

二维线性相位FIR数字滤波器的优化设计

该文提出了一种用神经网络算法来设计二维线性相位数字滤波器的新方法。通过分析二维FIR线性相位滤波器的幅频响应特性,建立了神经网络算法。根据给定的幅频响应指标,按该算法可获得滤波器系数。为保证该算法的稳定性,提出并证明了该算法的收敛定理。文中给出了圆对称和矩形对称二维低通线性相位FIR数字滤波器优化设计实例。计算机仿真结果表明由该方法设计的二维数字滤波器,通带和阻带范围波动小,所需计算量非常少,稳定性强,因而是一种优异的设计方法。     

On an inviable approach for derivation of 2-D stability tests

A tabular stability test for two-dimensional (2-D) discrete systems that was published in these Transaction is shown to be not correct. It is also shown that the claimed new method that it introduced to extend stability conditions from one-dimensional (1-D) to 2-D systems relies on a mathematically inviable argument. The paper tries to find a similar but correct algorithm and stability conditions. The outcome of the search after a stability test with similar algorithm is a variant of the Maria-Fahmy 2-D stability test for which a more concise set of necessary and sufficient conditions for stability are obtained. The search after stability conditions of similar appearance that can be posed on the correct algorithm, yields new necessary conditions for 2-D stability that resemble stability conditions associated with the "reflection coefficient" parameters in the 1-D Schur test.     

A Method for Computing the 2-D Stability Margin Based on a New Stability Test for 2-D Systems

In this paper, a new method to compute the stability margin of 2-D (two-dimensional) discrete systems is considered. The method is based on a recently proposed 2-D stability test by the author. Illustrative examples are also included.     

H∞ filtering of 2-D discrete systems

This paper deals with H_∞ filtering of two-dimensional (2-D) linear discrete systems described by a 2-D local state-space (LSS) Fornasini-Marchesini (1978) second model. Several versions of the bounded real lemma of the 2-D discrete systems are established. The 2-D bounded real lemma allows us to solve the finite horizon and infinite horizon H_∞ filtering problems using a Riccati difference equation or a Riccati inequality approach. Further a solution to the infinite horizon H_∞ filtering problem based on a linear matrix inequality (LMI) approach is developed. Our results extend existing work for one-dimensional (1-D) systems to the 2-D case and give a state-space solution to the bounded realness of 2-D discrete systems as well as 2-D H_∞ filtering for the first time. Numerical examples are given to demonstrate the Riccati difference equation approach to the 2-D finite horizon H_∞ filtering problem and the LMI approach to the 2-D infinite horizon H_∞ filtering problem     

Partial realization of 2-D discrete linear system and 2-D Padeapproximation and reduction of 2-D rational transfer function

A method is presented for determining the unknown degree and system function of any 2-D discrete linear shift-invariant system characterized by a 2-D impulse response array, i.e., the coefficients of the formal double power series that are obtained by expanding a rational transfer function. Problems of 2-D Pade approximation and 2-D system reduction can be solved by the same method by making a reasonable assumption in the context of 2-D linear systems theory. The method is based on a 2-D extension of the Berlekamp-Massey algorithm for synthesis of linear feedback shift registers. It gives a novel approach to identification and approximation of 2-D linear systems and is comparable in efficiency with other methods for 2-D rational approximation based on the block Toeplitz and block Hankel matrices     

基于截短ARQ协议的协作分集系统吞吐量研究

研究协作分集通信系统的跨层设计使系统吞吐量最大化.首先推导基于截短ARQ协议的协作分集和两跳系统的吞吐量理论表达式,揭示数据包长度和调制方式对系统吞吐量的影响,在此基础上用自适应技术优化系统性能,采用连续二维优化求出了吞吐量的最大值,进而提出了实用的二维离散吞吐量优化算法,该算法的优化结果与吞吐量最大值相差很小,最后提出了计算量更小的一维离散优化算法,且其吞吐量性能损失也很小.     

Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities

New criteria for the global asymptotic stability of the uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space model under various combinations of overflow and quantization nonlinearities are established. Sufficient conditions for the uncertain 2-D discrete systems to be free of overflow oscillations under a generalized overflow arithmetic are presented.     

On the stability preserving property of the double bilinear transformation on a class of 2-D transfer functions

This paper addresses the BIBO (bounded-input bounded-output) stability of a class of discrete 2-D quarter-plane filters in the presence of nonessential singularities of the second kind (NSSK's) on the unit bidisk. Conditions under which the double bilinear transformation (DBT) preserves stability are derived. The results presented here also extend the class of systems whose stability can be predicted. Use of the inverse DBT to produce a continuous equivalent of the discrete 2-D transfer function allows easy application of a continuous-domain equivalent of a criterion developed by Dautov. The necessary and sufficient condition for stability derived in this work provides a simple check for the class of systems under consideration. From this class of systems, it is also possible to construct stable pairs of mutually inverse transfer functions.     

Singular systems of partial difference equations

Sufficient conditions for the existence and uniqueness of solutions of singular systems of 2-D difference equations with constant coefficients are formulated. Linear transformation of the matrix coefficients leads to recursive forms of such systems of equations. The results are applied to standard 2-D state-space models of discrete systems and sufficient conditions of BIBO stability of these singular systems are obtained.