一类平面齐次多项式系统的局部相图

平面系统在动力系统的研究中起着重要的和基础的作用．在实系数系统情况下,本文利用奇点指数和牛顿多边形方法,讨论了一类平面齐次多项式系统在其孤立点附近的相图,同时给出一些奇点稳定的充要条件．     

具有饱和因子的时滞广义系统的鲁棒 H SymboleB@ 控制

研究了一类具有饱和因子并含有不确定参数的变时滞广义系统的时滞相关鲁棒H∞控制,系统的状态方程和输出方程均带有时滞,且状态方程的输入和输入时滞中均含饱和因子.通过构造Lya-punov-Krasovskii泛函,利用线性矩阵不等式方法和矩阵奇异值理论,给出了时滞广义系统正则、无脉冲、渐进稳定且满足H∞范数小于给定界γ的充分条件,并给出了H∞控制器的设计方法 .数值算例说明了本文所提方法具有更小的保守性.     

多时滞环状神经网络的稳定性

本文针对—个带自反馈的多时滞环状神经网络系统,给出了系统平凡解稳定与不稳定的条件,讨论了平凡解对应特征方程在不同参数条件下的正实部根的个数以及正实部根个数随参数变动的变化规律.     

Hilbert空间中二阶广义分布参数系统的反馈控制与极点配置

应用泛函分析及算子理论方法讨论了Hilbert空间中二阶广义分布参数系统的反馈控制与极点配置问题,通过构造状态反馈的具体形式使所得闭环系统实现无限多个极点的配置;利用有界线性算子的广义逆给出了问题的解及解的构造性表达式;这对广义分布参数系统的极点配置研究具有重要的理论价值.     

轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法

在考虑初始张力和轴向速度简谐涨落的情况下,利用含预应力三维变形体的运动方程,建立了轴向变速运动弦线横向振动的非线性控制方程,材料的粘弹性行为由Kelvin模型描述．利用匀速运动线性弦线的模态函数构造了变速运动非线性弦线复模态Galerkin方法的基底函数,并借助构造出来的基底函数研究了复模态Galerkin方法在轴向变速运动粘弹性弦线非线性振动分析中的应用．数值结果表明,复模态Galerkin方法相比实模态Galerkin方法对变系数陀螺系统有较高的收敛速度．     

ARMAX系统不外加输入激励的辨识

本文在不外加输入激励情况下，讨论了开环不稳定和非最小相位的ARMAX系统系数的一致估计．所用方法是用适应镇定的办法，使得闭环系统成为平稳可逆的ARMA过程，然后利用Yule-Walker方程给出闭环系统系数的一致估计，而把求开环系统系数的一致估计归结为解一组线性代数方程。     

一阶广义分布参数系统的极点配置问题

本文讨论了一阶广义分布参数系统的极点配置问题,应用算子的广义逆给出了问题的解及解的构造性表达式．     

方阵特征值之分布及其在稳定性理论中的应用

特征值实部全分布于复平面左半部之实方阵称为稳定阵(*),本文给出一类被称为实TD阵与另一类被称为实CTD阵是稳定阵的充要条件,并给出当方程AX XA′=-I(I为单位阵)的解X是实TD阵或实CTD阵时,A是稳定阵的充分条件。     

《中立型时滞抛物系统稳定性》的一个注记

给出了标题所述文章的一个注记，指出其中的主要结果(定理5)无意义或不成立.并给出了一类时滞抛物系统稳定的参数区域．     

输入受限系统的可控度及其在飞行控制中的应用

可控性是现代控制理论中最重要的概念之一,但是可控性只能给出系统可控或不可控的结论,而不能给出系统可控的程度.要回答这个问题,需要对可控性进行定量化描述.文章针对可控性的定量化指标的研究进行了调研和综述.在调研的基础上,将可控度主要分为三类:基于可控性矩阵的可控度,模态可控度,状态范数可控度.另外,文章重点讨论了输入受限系统的可控度问题以及可行的研究.最后,分析研究了可控度在飞行控制中飞行器执行器配置,容错控制分析,航路规划以及飞行安全监控中的应用.     

Estimating reachable sets for two-dimensional linear discrete systems

We are concerned with the problem of estimating the reachable set for a two-dimensional linear discrete-time system with bounded controls. Different approaches are adopted depending on whether the system matrix has real or complex eigenvalues. For the complex eigenvalue case, the quasiperiodic nature of minimum time trajectories is exploited in developing a simple, but often accurate, procedure. For the real eigenvalue case, over estimates of reachable sets can be trivially obtained using a decomposition method.The second author was supported by funds supplied by the John M. Bennett Faculty Fellowship, Trinity University, San Antonio, Texas.     

求解陀螺系统特征值问题的收缩二阶Lanczos方法

本文研究陀螺系统特征值问题的数值解法,利用反对称矩阵Lanczos算法,提出了求解陀螺系统特征值问题的二阶Lanczos方法.基于提出的陀螺系统特征值问题的非等价低秩收缩技术,给出了计算陀螺系统极端特征值的收缩二阶Lanczos方法.数值结果说明了算法的有效性.     

A new block preconditioner for complex symmetric indefinite linear systems

Using the equivalent block two-by-two real linear systems and relaxing technique, we establish a new block preconditioner for a class of complex symmetric indefinite linear systems. The new preconditioner is much closer to the original block two-by-two coefficient matrix than the Hermitian and skew-Hermitian splitting (HSS) preconditioner. We analyze the spectral properties of the new preconditioned matrix, discuss the eigenvalue distribution and derive an upper bound for the degree of its minimal polynomial. Finally, some numerical examples are provided to show the effectiveness and robustness of our proposed preconditioner.     

对称不定系统的一类预处理子的注记

由于对称正定系统已有很多有效的求解方法,因此将对称的、或者非对称的不定系统转化为对称正定系统就成为解决这类问题的方法之一构造了一类简洁有效的预处理子,将对称不定系统转化为对称正定型,研究了所得预处理系统的谱性质,估计了其谱条件数,推广了现有结论.     

Linear system identification via an asymptotically stable observer

This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero corresponding to a deadbeat observer. In this formulation, the Markov parameters of the observer are first identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to realize a state space model of the system. The basic mathematical formulation is derived, and numerical examples are presented to illustrate the proposed method.     

Design of $n$-dimensional multi-scroll Jerk chaotic system and its performances

Based on three-order Jerk and high-order Jerk chaotic systems, a general approach is proposed to generate $n$-dimensional multi-scroll Jerk chaotic attractors via nonlinear control. Dynamics of the $n$-dimensional multi-scroll Jerk chaotic systems are analyzed by means of the largest Lyapunov exponent and multi-scale permutation entropy complexity. As an experimental verification, four-dimensional Jerk chaotic attractors are implemented by analog circuits. Results of the numerical simulation are consistent with that of the hardware experiments. It shows that the method of obtaining complex Jerk chaotic attractors is effective.     

Singuläre S-hermitesche Rand-Eigenwertprobleme

The theory of singular self-adjoint eigenvalue problems developed by Weyl [13], Stone [12], Kodaira [2] and others has been generalized by A. Schneider [8], [9], [10], [11] to real S-hermitian systems of differential equations with real boundary conditions. Here the theory of singular S-hermitian boundary-value problems for arbitrary complex systems of differential equations with complex boundary conditions is developed. Moreover the boundary conditions are allowed to depend linearly on the eigenvalue-parameter.     

线性系统的输出反馈特征结构配置——具有不可控不可观模态的情形

本文考虑具有不可控不可观模态的线性系统的输出反馈特征结构配置问题。根据文中给出的矩阵方程AV＋BW＝VF的一种显式参数解，得到了线性系统的输出反馈特征结构配置的一种参数化方法，本文没有对系统附加能控能观条件，在[AB]能控的条件下，本文得到的矩阵方程的解是文[5]中定理2的结果，在[AB]能控且[AC]能观的条件下，本文得到的输出反馈特征结构配置方法是文[6]在系统为定常时算法Ⅱ的结果。     

Interplay between Riccati,Ermakov, and Schrödinger equations to produce complex‐valued potentials with real energy spectrum

Nonlinear Riccati and Ermakov equations are combined to pair the energy spectrum of 2 different quantum systems via the Darboux method. One of the systems is assumed Hermitian, exactly solvable, with discrete energies in its spectrum. The other system is characterized by a complex‐valued potential that inherits all the energies of the former one and includes an additional real eigenvalue in its discrete spectrum. If such eigenvalue coincides with any discrete energy (or it is located between 2 discrete energies) of the initial system, its presence produces no singularities in the complex‐valued potential. Non‐Hermitian systems with spectrum that includes all the energies of either Morse or trigonometric Pöschl‐Teller potentials are introduced as concrete examples.     

Stabilization of nonlinear systems in compound critical cases

In this paper, we study the stabilization of nonlinear systems in critical cases by using the center manifold reduction technique. Three degenerate cases are considered, wherein the linearized model of the system has two zero eigenvalues, one zero eigenvalue and a pair of nonzero pure imaginary eigenvalues, or two distinct pairs of nonzero pure imaginary eigenvalues; while the remaining eigenvalues are stable. Using a local nonlinear mapping (normal form reduction) and Liapunov stability criteria, one can obtain the stability conditions for the degenerate reduced models in terms of the original system dynamics. The stabilizing control laws, in linear and/or nonlinear feedback forms, are then designed for both linearly controllable and linearly uncontrollable cases. The normal form transformations obtained in this paper have been verified by using code MACSYMA.