An elementary proof of the Routh-Hurwitz stability criterion

This paper presents an elementary proof of the well-known Routh-Hurwitz stability criterion. The novelty of the proof is that it requires only elementary geometric considerations in the complex plane. This feature makes it useful for use in undergraduate control system courses.Research supported by Hughes Aircraft Company, El Segundo, California 90245, USA, and the National Science Foundation under Grant ECS 21818.     

Design and stability analysis of a rate control algorithm using the Routh-Hurwitz stability criterion

Feedback delays arise in the control of a computer network-from the information transfer process itself and from the processing of control signals at the network nodes. Flow control of data sources in a computer network often results in a time-delayed control problem. Feedback delay reduces the stability of a system. In this paper we discuss how to use the Routh-Hurwitz stability criterion to design and analyze the stability of a flow control algorithm with feedback delay.     

Generalisation of the Routh-Hurwitz criterion and its applications

A generalisation of the Routh-Hurwitz stability criterion for testing the presence of unstable roots of a polynomial with complex coefficients is presented. Numerical examples are given to illustrate the application of the generalisation.     

Analysis of microstrip discontinuities by FDTD method combined with SOC technique

In this paper, the application of the finite-difference time-domain (FDTD) algorithm combined with the short-open calibration SOC technique to three-dimensional microstrip discontinuity is presented. This SOC technique is directly accommodated in the FDTD algorithm. It is used to remove the unwanted parasitic errors brought by the approximation of the impressed voltage sources and the feed lines. The FDTD is formulated in such a way that the port voltages and currents are explicitly represented through relevant network matrices. This new method is also used to analyze finite periodic structures. The scattering parameters of the whole periodic structure can be approximately obtained through analyzing only one cell of it. The results for microstrip discontinuities and finite periodic structures are compared with the conventional FDTD method.     

3-D FDTD method with weakly conditional stability

A novel 3-D FDTD method with weakly conditional stability is presented. The time step in this method is only determined by one space discretisation. Compared with the ADI-FDTD method, this method has better accuracy and higher computation efficiency. CPU time for this weakly conditionally stable FDTD method can be reduced to about 3/4 of that for the ADI-FDTD scheme     

基于混合计算方法的脉冲超宽带穿墙散射建模

基于时域射线追踪技术(TD-Ray)和时域有限差分方法(FDTD),提出了一种可以对穿墙传播环境中的组合尺寸结构进行快速电磁散射建模的混合计算方法。混合方法针对冲激/脉冲超宽带(IR-UWB)信号时域极窄的特点,利用TD-Ray技术来计算电大尺寸的规则墙体结构及室内空间的传播过程,避免了FDTD方法在电大结构和空间传播上过于精细的网格划分,提高了计算效率并减少内存需求。混合方法同时又结合FDTD方法对室内较小尺度的复杂损耗结构进行计算,可以解决TD-Ray技术在复杂损耗结构电磁建模上存在的困难,从而保证了电磁散射的计算精度。通过应用算例验证了该方法在电大电小组合结构电磁散射建模上的有效性,对比表明该方法得到的穿墙人体目标平均雷达散射截面(RCS)计算结果与实测数据吻合较好。     

Inverse Routh-Hurwitz array solution to the inverse stability problem

In this letter, a general method will be given whereby the inverse Routh-Hurwitz array may be constructed. This gives a solution to the inverse stability problem as first posed by Jarominek.     

An efficient and accurate technique for the incident-waveexcitations in the FDTD method

An efficient technique to improve the accuracy of the finite-difference time-domain (FDTD) solutions employing incident-wave excitations is developed. In the separate-field formulation of the FDTD method, any incident wave may be efficiently introduced to the three-dimensional (3-D) computational domain by interpolating from a one-dimensional (1-D) incident-field array (IFA), which is a 1-D FDTD grid simulating the propagation of the incident wave. By considering the FDTD computational domain as a sampled system and the interpolation operation as a decimation process, signal-processing techniques are used to identify and ameliorate the errors due to aliasing. The reduction in the error is demonstrated for various cases. This technique can be used for the excitation of the FDTD grid by any incident wave. A fast technique is used to extract the amplitude and the phase of a sampled sinusoidal signal     

Full-wave modelling of coaxial cables by FDTD technique

Coaxial cables are commonly used in microwave systems but are difficult to model rigorously in the finite-difference time-domain (FDTD) method, particularly with coarse meshes. Various techniques are investigated and the optimum method identified. In addition, attention is paid to strategies for the computation of the characteristic impedance.     

Generalized analysis of stability and numerical dispersion in thediscrete-convolution FDTD method

A simple technique is described for determining the stability and numerical dispersion of finite-difference time-domain (FDTD) calculations that are linear, second-order in space and time, and include dispersion by the discrete convolution method. The technique is applicable to anisotropic materials. Numerical examples demonstrate the accuracy of the technique for several anisotropic and/or dispersive materials     

Analyzing electromagnetic structures with curved boundaries onCartesian FDTD meshes

In this paper, a new finite-difference time-domain (FDTD) algorithm is investigated to analyze electromagnetic structures with curved boundaries using a Cartesian coordinate system. The new algorithm is based on a nonorthogonal FDTD method. However, only those cells near the curved boundaries are calculated by nonorthogonal FDTD formulas; most of the grid is orthogonal and can be determined by traditional FDTD formulas. Therefore, this new algorithm is more efficient than general nonorthogonal FDTD schemes in terms of computer resources such as memory and central processing unit (CPU) time. Simulation results are presented and compared to those using other methods     

Numerical stability of nonorthogonal FDTD methods

In this paper, a sufficient test for the numerical stability of generalized grid finite-difference time-domain (FDTD) schemes is presented. It is shown that the projection operators of such schemes must be symmetric positive definite. Without this property, such schemes can exhibit late-time instabilities. The origin and the characteristics of these late-time instabilities are also uncovered. Based on this study, nonorthogonal grid FDTD schemes (NFDTD) and the generalized Yee (GY) methods are proposed that are numerically stable in the late time for quadrilateral prism elements, allowing these methods to be extended to problems requiring very long-time simulations. The study of numerical stability that is presented is very general and can be applied to most solutions of Maxwell's equations based on explicit time-domain schemes     

光子晶体波导的FDTD分析

介绍了光子晶体波导的原理,然后运用时域有限差分方法(FDTD法)分析了二维光子晶体波导的传输特性,最后运用Matlab语言实现了二维光子晶体波导的仿真,使用的是TM模.     

FDTD分析准八木天线的算法实现

介绍时域有限差分（FDTD）法计算准八木天线驻波比的算法实现方法。文中利用模型描述文件对天线进行了建模和网格划分;将各向异性完全匹配层（UPML）吸收边界分区编写,并利用区域的对称性简化了程序;采用带内阻的电压源作为激励源;最后从总电压中分离出入射电压和反射电压,得到了准八木天线的驻波比。实际制作了一个准八木天线并进行了测试,计算结果与实测结果基本一致,表明该实现方法是正确和有效的。     

Sensitivity analysis with the FDTD method on structured grids

We propose an adjoint-variable approach to design-sensitivity analysis with time-domain methods based on structured grids. Unlike conventional adjoint-based methods, it does not require analytical derivatives of the system matrices. It is simple to implement with existing computational algorithms such as the finite-difference time-domain (FDTD) technique. The resulting FDTD algorithm produces the response and its gradient in the design parameter space with two simulations regardless of the number of design parameters. The proposed method is validated by the adjoint-based FDTD analysis of waveguide structures with metallic boundaries.     

A hybrid technique based on combining ray tracing and FDTD methodsfor site-specific modeling of indoor radio wave propagation

The paper presents a hybrid technique based on combining ray tracing and finite-difference time-domain (FDTD) methods for site-specific modeling of indoor radio wave propagation. Ray tracing is used to analyze the wide area and FDTD is used to study areas close to complex discontinuities where ray-based solutions are not sufficiently accurate. The hybrid technique ensures improved accuracy and practicality in terms of computational resources at the same time since FDTD is only applied to a small portion of the entire modeling environment. Examples of applying the method for studying indoor structures and penetration of wave from outdoor to indoor are given at 2.4 GHz. Numerical results are compared with known exact solutions or results of the full wave analysis or traditional ray model to demonstrate the accuracy, efficiency, and robustness of the novel method. Numerical results are also compared with reported measurement results for waves at 1.29 GHz penetrating an external wall with metal-framed windows. Cumulative distributions of field envelope obtained from the hybrid method show close resemblance to the Rayleigh distribution, which conforms to the reported measurement results     

ARMA-based time-signature estimator for analyzing resonantstructures by the FDTD method

We propose an algorithm for estimation of the optimal “system” parameters of time sequences (TSs) computed by the finite-difference time-domain (FDTD) method, with the goal of accurate representation of the time-signature using low-order models. The FDTD method requires computation of very long time sequences to accurately characterize the slowly decaying transient behavior of resonant structures. Therefore, it becomes critical to investigate methods of reducing the computational time for such objects. Several researchers have argued that the FDTD-TS can be modeled as the impulse response (IR) of an autoregressive moving average (ARMA) transfer function. However, it is known that determination of ARMA parameters by IR matching is a complex nonlinear optimization problem. Hence, many existing methods in EM literature tend to use Prony-based, linear predictor-type spectrum estimation algorithms, which minimize a linearized “equation error” criterion that approximates the true nonlinear model-fitting error criterion. As a result, significantly high model orders are needed by these methods to achieve good corroboration in the frequency domain, especially when a magnitude spectrum has deep nulls or notches. We propose to use a deterministic ARMA approach, which minimizes the true nonlinear criterion iteratively, and attains significantly improved IR fit over Prony's (1795) method using fewer ARMA model parameters. For a given time-sequence of an analyzed circuit, the issues of model order selection and choice of decimation factor are also addressed systematically. The improved performance of the proposed algorithm is demonstrated with transient simulation and signal analysis of microstrip structures which manifest deep nulls in the frequency domain