时滞切换系统的时滞依赖稳定

首先利用多Lyapunov 函数方法, 分析常时滞切换系统的时滞依赖稳定性, 并给出此系统时滞依赖稳定的充分条件及切换律的设计; 然后运用共同Lyapunov 函数方法, 研究一类时变时滞切换系统的时滞依赖稳定性, 也给出此系统时滞依赖稳定的充分条件及切换律的设计. 所得结果均可用线性矩阵不等式方法求解. 最后通过仿真验证了结论的正确有效性.     

Stability of linear multistep methods for delay integro-differential equations

This paper is concerned with the numerical solution of delay integro-differential equations. The adaptation of linear multistep methods is considered. The emphasis is on the linear stability of numerical methods. It is shown that every A-stable, strongly 0-stable linear multistep method of Pouzet type can preserve the delay-independent stability of the underlying linear systems. In addition, some delay-dependent stability conditions for the stability of numerical methods are also given.     

多输入多输出线性定常系统稳定裕度的分析与改进

针对多输入多输出(MIMO)控制系统的稳定裕度求解问题,首先分析了现有的回差阵奇异值法这一计算方法,并得到其解决单输入单输出(SISO)系统的稳定裕度结论,在此基础上,提出两种基于系统回差阵的稳定裕度改进方法;一种是在有限条件下利用矩阵的特征值代替奇异值来建立与稳定裕度关系的策略,另一种是利用系统逆回差阵的行列式,通过求其奇异值来计算系统稳定裕度;最后结合工程实例,通过数值仿真验证两种稳定裕度计算方法相比原方法都有不同程度的改进,而且三种方法可以结合起来进行分析,最大化的减小系统稳定裕度结果的保守性.     

基于RKNd算法的暂态稳定性快速数值计算方法

RKNd方法是一类新的数值积分方法。在相同级数条件下,RKNd方法可达到的最高代数阶比传统的Runge—Kutta方法以及Runge—Kutt—Nystrom方法均高,而且具有更高的计算效率。将RKNd方法引入电力系统暂态稳定性数值计算。以IEEEl45节点电力系统为例,通过数值实验将新方法与电力系统分析中常用的传统数值计算方法进行了对比分析。数值实验结果表明,RKNd方法在计算精度和计算效率等方面均具有明显的优势,N而更适合于电力系统暂态稳定性及相似问题的数值计算。     

模糊系统稳定性

简要综述了模糊控制系统的稳定性分析方法,详细介绍了这些方法的概念和原理,分析总结了每种方法的适用对象及优缺点,最后展望了这一领域今后的研究方向.     

An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation

To date, the only effective approach for computing guaranteed bounds on the solution of an initial value problem (IVP) for an ordinary differential equation (ODE) has been interval methods based on Taylor series. This paper derives a new approach, an interval Hermite-Obreschkoff (IHO) method, for computing such enclosures. Compared to interval Taylor series (ITS) methods, for the same stepsize and order, our IHO scheme has a smaller truncation error, better stability, and requires fewer Taylor coefficients and high-order Jacobians.The stability properties of the ITS and IHO methods are investigated. We show as an important by-product of this analysis that the stability of an interval method is determined not only by the stability function of the underlying formula, as in a standard method for an IVP for an ODE, but also by the associated formula for the truncation error.     

Sufficient Conditions for Stability of Periodic Linear Impulsive Delay Systems

For a linear periodic system with impulsive action and delay, new approaches to the study of stability were proposed on the basis of the methods of spectral theory of linear operators, direct Lyapunov method, and N.G. Chetaev method for construction of the Lyapunov functions for the periodic linear systems, as well as the perturbation method for construction of the Lyapunov functions. These methods underlie the sufficient conditions for asymptotic stability of the linear periodic systems with impulsive action and delay. We gave some illustrative examples of studying stability of such systems under different assumptions about the dynamic properties of the continuous and discrete components of the impulsive system.     

Matrix Stability of Multiquadric Radial Basis Function Methods for Hyperbolic Equations with Uniform Centers

The fully discretized multiquadric radial basis function methods for hyperbolic equations are considered. We use the matrix stability analysis for various methods, including the single and multi-domain method and the local radial basis function method, to find the stability condition. The CFL condition for each method is obtained numerically. It is explained that the obtained CFL condition is only a necessary condition. That is, the numerical solution may grow for a finite time. It is also explained that the boundary condition is crucial for stability; however, it may degrade accuracy if it is imposed.     

Systems with a switch and estimation of absolute stability region

Two methods are proposed for estimation of absolute stability region in the space of parameters. The first method uses nontrivial necessary conditions, which follow from stability of switching systems. The second method is a modification of the harmonic balance approach; it is used for approximate determination of existence of periodic modes that arise when stability is lost.     

Stability analysis of linear time-varying systems

This paper addresses the issue of the stability of linear time-varying systems. Recently developed elemental perturbation bound analysis is extended to obtain stability bounds on the parameters of linear time-varying systems. In particular, systems governed by the Mathieu equation are considered. The bounds obtained with the proposed method are compared with those of the circle criterion and matrix decomposition methods. The proposed method is computationally simple and the bounds obtained fare well with the other methods considered.     

Direct method for transient stability studies in power system analysis

This paper deals with recent advances in developing direct methods for studying the transient stability problem of single-machine and multimachine power systems. The paper starts out with the construction of the mathematical model that is usually employed in the analyis of power system transient stability. Computer simulation methods are then briefly discussed, and it is indicated why accurate direct methods for transient stability investigations would be most welcome. It is shown that the classical direct methods, which are based on energy considerations, can be derived and generalized by means of Lyapunov's second method. The main purpose of the paper is to give an exposition of the interesting results that have been obtained by applying Lyapunov's second method to the transient stability problem of single-machine and multimachine power systems. In the final portion of the paper some areas for further research are discussed.     

Transient stability region of power systems using series expansion of Lyapunov functions

In this paper, a method is proposed for improving the accuracy of the stability criterion by enlarging the estimation of the stability region determined by means of Lyapunov's direct method using series expansion, and by putting it closer to the actual stability region. The Lyapunov function obtained by energy integration is used as the first estimation. The method is applied to a single-machine infinite bus power system, and the stability domain in the δ-ω plane is shown together with the actual stability domain obtained by numerical integration. It is shown that the application of the proposed method results in a considerable improvement in the stability boundary estimation over that given by the original Lyapunov function. Zubov's method, which obtains an accurate stability boundary using the series expansion, is related to the method proposed in this paper. The last section is, therefore, devoted to comparing the two methods and examining the possibility of their application to multi-machine power systems.     

Stochastic projective methods for simulating stiff chemical reacting systems

In this paper, stochastic projective methods are proposed to improve the stability and efficiency in simulating stiff chemical reacting systems. The efficiency of existing explicit tau-leaping methods can often severely be limited by the stiffness in the system, forcing the use of small time steps to maintain stability. The methods presented in this paper, namely stochastic projective (SP) and telescopic stochastic projective (TSP) method, can be considered as more general stochastic versions of the recently developed stable projective numerical integration methods for deterministic ordinary differential equations. SP and TSP method are developed by fully re-interpreting and extending the key projective integration steps in the deterministic regime under a stochastic context. These new stochastic methods not only automatically reduce to the original deterministic stable methods when applied to simulating ordinary differential equations, but also carry the enhanced stability property over to the stochastic regime. In some sense, the proposed methods are stochastic generalizations to their deterministic counterparts. As such, SP and TSP method can adopt a much larger effective time step than is allowed for explicit tau-leaping, leading to noticeable runtime speedup. The explicit nature of the proposed stochastic simulation methods relaxes the need for solving any coupled nonlinear systems of equations at each leaping step, making them more efficient than the implicit tau-leaping method with similar stability characteristics. The efficiency benefits of SP and TSP method over the implicit tau-leaping is expected to grow even more significantly for large complex stiff chemical systems involving hundreds of active species and beyond.     

Fourier analysis of semi-discrete and space–time stabilized methods for the advective–diffusive–reactive equation: II. SGS

In this paper, stability and accuracy of various transient subgrid scale (SGS) stabilized methods are analyzed for the advection–diffusion–reaction equation. The methods studied are based on semi-discrete and time-discontinuous space–time versions of the SGS method, an approximation of the variational multiscale method. Also, predictor multi-corrector algorithms of the above methods are analyzed. Within this context, the diagonally implicit treatment of dissipative source terms, which was shown in the first paper of the series to enhance both, stability and accuracy of explicit methods, is explored in this paper for the SGS method. It will be shown that the parent SUPG and SGS methods perform very similarly. That mass lumping may improve the accuracy of explicit methods. And finally, the most attractive options for the explicit integration of equations with source terms will be presented.     

Revisiting four approximation methods for fractional order transfer function implementations: Stability preservation,time and frequency response matching analyses

Due to high computational load of ideal realization of fractional order elements, fractional order transfer functions are commonly implemented via integer-order, limited-band approximate models. An important side effect of such a non-ideal fractional order controller function realization for control applications is that the approximate fractional order models may deteriorate practical performance of optimal control tuning methods. Two major concerns come out for approximate realization in fractional-order control. These are stability preservation and model response matching properties. This study revisits four fundamental fractional order approximation methods, which are Oustaloup's method, CFE method, Matsuda's method and SBL fitting method, and considers stability preservation, time and frequency response matching performances. The study firstly presents a detailed review of Oustaloup's method, CFE method, Matsuda's method. Then, a modified version of SBL fitting method is presented. The stability preservation properties of approximation methods are investigated according to critical root placements of corresponding approximation method. Stability issue is highly significant for control applications. For this reason, a detailed analysis and comparision of stability preservation properties of these four approximation methods are investigated. Moreover, approximate implementations of an optimally tuned FOPID controller function are performed according to these four methods and compared for closed loop control of a large time delay system. Findings of this study indicate a fact that approximate models can considerably influence practical performance of optimally tuned FOPID control systems and ignorance of limitations of approximation methods in optimal tuning solutions can significantly affect real world performances.     

New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction

Three well-known stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation method—are consequently shown to be closely related. Previously observed properties of the methods are explained by treating them as multipoint approximants, and the significance of using expansion points on the imaginary axis is shown to be central to stability preservation.     

广义系统的渐近稳定性与镇定

利用Lyapunov方法研究广义系统的渐近稳定性及相关的镇定问题.得到了渐近稳定的条件及镇定方法.     

Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem

Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite-element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently discovered unusual stability properties of the linearized force-based quasicontinuum (QCF) approximation, especially its indefiniteness, present a challenge to the development of efficient and reliable iterative methods.We present analytic and computational results for the generalized minimal residual (GMRES) solution of the linearized QCF equilibrium equations. We show that the GMRES method accurately reproduces the stability of the force-based approximation and conclude that an appropriately preconditioned GMRES method results in a reliable and efficient solution method.     

信息检索策略性能的云模型评价方法

在信息检索中,目前常见的评价方法仅能反映检索策略的平均性能,不能反映策略的稳定性、随机性等问题,因此对检索策略的评价不够全面。本研究提出了基于云模型的检索策略评价方法,该方法建立了定性评价和定量数据之间的自然转换,这种转换是通过严格的数学方法来实现的,用该方法评价检索策略,不仅能反映策略的平均性能,而且能反映策略的稳定性。实验数据表明,该方法是切实可行的,评价结果更加逼近实际情况。该方法也可以用于文本分类策略的评价。     

The investigation algorithm of stability of periodic oscillations in the problem for the Andronov-Hopf bifurcation

A new method for analysis of the stability of free oscillations under the conditions of the Andronov-Hopf bifurcation is suggested. In contrast to commonly applied methods, the algorithm suggested does not require the construction of integral varieties and the transition to normal forms. The algorithm is based on the comparison between the characters of stability of the stationary state of the system and the free oscillations being born. The method suggested enables us to simplify essentially the analysis of stability and obtain simple explicit criteria of stability and instability, and also define the type of bifurcation.