On a Non-homogeneous Singular Linear Discrete Time System with a Singular Matrix Pencil

In this article, we study the initial value problem of a non-homogeneous singular linear discrete time system whose coefficients are either non-square constant matrices or square with an identically zero matrix pencil. By taking into consideration that the relevant pencil is singular, we provide necessary and sufficient conditions for existence and uniqueness of solutions. More analytically we study the conditions under which the system has unique, infinite and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally we provide some numerical examples based on a singular discrete time real dynamical system to justify our theory.     

线性时滞系统一致渐近稳定的时滞界

本文提出一种确定线性时滞系统Ｘ（ｔ）＝Ａｘ（ｔ）＋Ｂｘ（ｔ－τ）稳定的时滞界的方法,从而得出了线性系统时滞相关稳定的充分条件,降低了有关判定系统稳定性的保守性和检验稳定性的复杂程度,文中并给出了确定时滞界的数值算示,数值计算结果表明了该算法的可行性和有效性。     

Modeling and Realization of n-Dimensional Linear Discrete Systems

Using a general model for multidimensional linear discrete systems, a new non-minimal real ARMA realization is given for n-dimensional systems in AR forms. A definition of minimality which is compatible with both the underlying theory and its engineering applications, and some necessary conditions for minimality of multidimensional systems are given.     

A Generalized Kalman Filter for 2D Discrete Systems

This paper studies the problem of state estimator design for stochastic twodimensional (2D) discrete systems described by the secondary 2D Fornasini-Marchesini odel subject to white noise in both the state and measurement equations. The aim is to design a 2D Kalman filter that minimizes the variance of the estimation error of the state vectors. An explicit formulation of the estimator is derived, based on which, an algorithm for the design of the desired Kalman filter is proposed. Finally, examples are provided to demonstrate the effectiveness of the proposed method.     

Sweep-Acquisition Time of Third-Order Generalized Tracking Systems

By using a quasi-stationary approximation a closed form expression is derived for the acquisition time of a third-order swept tracking system, with an arbitrary phase-detector characteristic and with nonideal as well as with ideal integrating filter, optimized for tracking or demodulation in the absence of noise with large initial detuning (relative to the noise bandwidth). For sinusoidal phase detector with ideal or nonideal filters, exact solutions confirm theoretical predictions.     

First–Order Representations of Discrete Linear Multidimensional Systems

The classical localstate–space models for discrete multidimensional linearsystems, as proposed by Roesser or Fornasini and Marchesini,require causality of the resulting transfer matrices. We considera generalization comprising non-causal systems, based on Willems'state-space behaviors. A vector of manifest and a vector of latentvariables are supposed to be linked via a first–order dynamicequation and a static equation. Any system of linear constant–coefficientpartial difference equations gives rise to such an ``output–nulling'(ON) representation. Controllable systems possess driving–variablerepresentations, which are the dual counterpart of ON repsin many aspects. We study these representations with respectto their minimality, observability and controllability, and wederive conditions for their reducibility to the standard input–state–outputsetting.     

A Generalized Fault Coverage Model for Linear Time-Invariant Systems

This paper proposes a fault coverage model for linear time-invariant (LTI) systems subject to uncertain input. A state-space representation, defined by the state-transition matrix, and the input matrix, is used to represent LTI system dynamic behavior. The uncertain input is considered to be unknown but bounded, where the bound is defined by an ellipsoid. The state-transition matrix, and the input matrix must be such that, for any possible input, the system dynamics meets its intended function, which can be defined by some performance requirements. These performance requirements constrain the system trajectories to some region of the state-space defined by a symmetrical polytope. When a fault occurs, the state-transition matrix, and the input matrix might be altered; and then, it is guaranteed the system survives the fault if all possible post-fault trajectories are fully contained in the region of the state-space defined by the performance requirements. This notion of guaranteed survivability is the basis to model (in the context of LTI systems) the concept of fault coverage, which is a probabilistic measure of the ability of the system to keep delivering its intended function after a fault. Analytical techniques to obtain estimates of the proposed fault coverage model are presented. To illustrate the application of the proposed model, two examples are discussed.     

一类网络环境下的离散线性系统的可靠性滤波器设计研究

本文对一类网络环境下的离散线性系统进行了可靠性滤波器设计,其中用一组随机变量来表示传感器的概率性失真,并综合考虑网络环境的时滞、错序、丢包等非理想服务质量,建立了包含传感器随机失真的系统模型;通过使用李亚普诺夫泛函稳定性理论和线性矩阵不等式技术给出了可靠性滤波器设计算法存在可行解的充分性条件,最后通过数值算例验证本文给出方法的有效性.     

Optimum Linear Constellation Precoding for Space Time Wireless Systems

Space Time Constellation Rotating Codes (STCRs) achieve a rate of 1 symbol/s/Hz and enjoy a diversity N _tN_r for arbitrary number of transmit and receive antennas N _t and N _r over quasi static fading channels. Optimum Unitary STCRs based on Algebraic design tools, which achieve the upper bound on coding gain for all linear precoders over Quadrature Amplitude Modulation (QAM) and Pulse Amplitude Modulation (PAM), are known only when the number of transmit antennas is power of two. In this paper we design optimum unitary LCPs for even number of transmit antennas. We also present some unitary precoders for odd number of transmit antennas which clearly out-perform the existing unitary non-optimum precoders. Performance results corroborate our analysis. Manav R. Bhatnagar was born in Moradabad, India in 1976. He did his B.E. in Electronics in 1997 and Master of Technology in Communications Engineering in 2005 from Indian Institute of Technology Delhi, India. He has worked as lecturer in Moradabad Institute of Technology, Moradabad, India from 1998--2003. He is currently pursuing PhD from Indian Institute of Technology Delhi, India. His research interests include Routing in Optical Networks, Signal Processing in Wireless Communications and Image Processing. He is a member of the IEEE. R Vishwanath was born in Hyderabad, India in 1982. He did his B.E. in Electronics and Communications Engineering from Birla Institute of Technology, Ranchi, India in 2002 and Master of Technology in Communications Engineering in 2005 from Indian Institute of Technology Delhi, India. Currently he is pursuing PhD from Indian Institute of Technology Delhi, India. His research interests include Routing in Optical Networks, Signal Processing, Wireless Communications and Image Processing. He is a member of the IEEE.     

广义Legendre序列的线性复杂度

广义Legendre序列具有良好的自相关性和较高的线性复杂度,论文研究了该类序列的构造特点,给出了它的一个等价定义,确定了b为自然排列和倒序排列时广义Legendre序列的线性复杂度和极小多项式,并将该结果推广至其他一般情况。     

A Note on Generalized Linear Phase Conditions for Causal FIR Systems

An alternative proof is presented for the necessary conditions for generalized linear phase in causal FIR systems, which appears to be somewhat crisper and more straightforward than the existing proofs available in the literature.     

基于Δ调制反馈离散时间系统的Hash函数研究

Δ调制反馈离散时间系统在一定的参数范围内出现混沌运动,其产生的混沌序列具有良好的伪随机性、遍历性和初值敏感性。文中基于该系统建立了一个带秘密密钥的Hash函数算法,算法以迭代初始点作为秘密密钥。实验表明:该方法简单,具有良好的单向散列性能,并能满足一定的安全性要求。     

基于△调制反馈离散时间系统的Hash函数研究

△调制反馈离散时间系统在一定的参数范围内出现混沌运动，其产生的混沌序列具有良好的伪随机性、遍历性和初值敏感性．文中基于该系统建立了一个带秘密密钥的Hash函数算法，算法以迭代初始点作为秘密密钥．实验表明：该方法简单，具有良好的单向散列性能，并能满足一定的安全性要求．     

Generalized Linear Mixed Models for Reliability Analysis of Multi-Copy Repairable Systems

The power law process (PLP) is usually applied to failure data from a single repairable system. When a system has a number of copies for analysis, the usual approach is to assume homogeneity among all system copies, and then to pool data from these copies. In the real world, however, it may be more reasonable to assume heterogeneity among the system copies. Therefore, this paper proposes a new generalized linear mixed model (GLMM), called PLP-GLMM, to analyse failure data from multi-copy repairable systems. In the PLP-GLMM, the underlying model for each system copy is assumed to be a PLP at Stage 1, and parameters vary among copies at Stage 2. The PLP-GLMM can make inferences about both the population, and each system copy when accounting for copy-to-copy variance. A modified Anderson-Darling test is adapted to the goodness-of-fit test of the PLP-GLMM. A numerical application is given to show the effectiveness of the model     

线性时滞系统可辨识性的探讨

可辨识性分析法是为具有时滞状态，可控输入和可观测输出的线性时滞系统开发的，该系统具有有限数量的集总延迟。文中阐述了提供充分不平稳输入信号时，线性时滞系统传递函数的在线辨识性，可控输入的不连续性对系统的马尔科夫参数可辨识性的决定性，系统传递函数的在线辨识性和系统的马尔科夫参数可辨识性的关系，分析了系统可辨识的条件和必需的输入信号特性，用一个例子说明了系统可辨识性理论的应用。     

Asymptotic Stability of a Class of Linear Discrete Systems with Multiple Independent Variables

This paper investigates the problem of asymptotic stability for a class of linear shift-invariant discrete systems with multiple independent variables. We establish the equivalence of this problem and that of robust stability for a class of ordinary linear shiftvarying discrete systems with the matrix uncertainty set defined by the coefficient matrices of the original system. On the basis of this equivalence, by using the variational method and Lyapunovs second method, necessary and sufficient conditions for asymptotic stability are obtained in different forms for the class of systems considered. The parametric classes of Lyapunov functions which define the necessary and sufficient conditions of asymptotic stability are determined. We use the piecewise linear polyhedral Lyapunov functions of the infinity vector norm type to derive an algebraic criterion for asymptotic stability of the given class of discrete systems in the form of solvability conditions of a set of matrix equations. A simple sufficient condition of asymptotic stability is also obtained which becomes necessary and sufficient for several special cases of the discrete systems under consideration.     

Real-Valued Discrete Gabor Transform of Linear TimeVarying Systems： Exact Representation and Approximation

An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existingalg orithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more edsily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.     

Some Considerations for Multiple-Unit Redundant Systems with Generalized Repair Time Distributions

The mean time to system failure (MTSF) for a 2-out-of-n system with repair is intuitively derived. The improvement factor, the ratio of the MTSF for a 2 out of n system with repair to that system without repair, is evaluated and its asymptotic behavior is studied.     

Robust H∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays

This paper considers the problem of robust H_∞ filtering for uncertain discrete-time stochastic systems with time-varying delays. The parameter uncertainties are assumed to be real time-varying norm-bounded in both the state and measurement equations. The problem to be addressed is the design of a stable filter that guarantees stochastic stability and a prescribed H_∞ performance level of the filtering error system for all admissible uncertainties and time delays. A sufficient condition for the existence of such filters is obtained in terms of a linear matrix inequality (LMI). For the case when this LMI is feasible, an explicit expression for a desired filter is given. An illustrative example is also provided to demonstrate the effectiveness and applicability of the proposed method.     

Calculation of the Second Order Settling Time in SISO Linear Systems

This paper clearly defines the second order settling time as a special and most important case of the generalized settling time. A new calculation procedure for second order settling time determination is developed, based on a decomposition of deterministic, random or mixed non-stationary signals in steady-state and transient components. A worked out example illustrates the computation procedure. The derived relations can be implemented in the form of computer programs. Although restricted to SISO linear systems, the procedure developed in this paper covers a lot of practical situations like those encountered in sensors and transducers modeling.