具有变时滞的离散切换系统的时滞依赖稳定性的新判据

This paper deals with the issues of robust stability for uncertain discrete-time switched systems with mode-dependent time delays.Based on a novel difference inequality and a switched Lyapunov function,new delay-dependent stability criteria are formulated in terms of linear matrix inequalities （LMIs） which are not contained in known literature.A numerical example is given to demonstrate that the proposed criteria improves some existing results significantly with much less computational effort.     

求解广义线性互补问题的光滑牛顿法(英文)

The extended linear complementarity problem(denoted by ELCP) can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed CHKS smoothing function, the ELCP is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is designed for solving the ELCP. The proposed algorithm is proved to be globally convergent under suitable assumptions.     

一类非线性切换系统的反馈镇定性

考虑了一类非线性切换系统的反馈镇定性.利用多Lyapunov函数递推设计方法使切换系统在任意切换信号下,都可找到相应的反馈控制器使其可镇定.     

波方程的边界镇定性的分析(英文)

利用乘子法研究了带有变系数的波方程的反馈镇定问题．文章中变系数ｑ（ｘ）分为两种情况：（Ｈ_１）ｑ和（Ｈ_２）ｑ．同时还引入了敏感反馈系数和波方程能量的指数衰减域．更为重要的是,本文统一和改善了一些以前已有的结果．     

U(4,Z)的自同构群(英文)

In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then （i） InnG ■ K ■ AutG;（ii） AutG/K≌=G₁×D₈×Z₂,where G₁=(a,b,c|a⁴=b²=c²=1,a^b=a^-1,[a,c]= [b,c]=1 ;（iii） K/Inn G≌=Z×Z×Z.     

一类差分方程性质的研究(英文)

This paper is concerned with the following rational difference equation xn+1=axn-bxn-1+ex2n/(cXn+dxn-1), with the initial conditions x-1 , x0 ∈ (0, +∞) and a, b, c, d, e ∈ R+ . Locally asymptotically stability, global attractively and boundedness character of the equilibrium point of the equation are investigated. Moreover, simulation is shown to support the results.     

时变线性系统的渐近稳定性的积分判据(英)

本文研究时变线性系统的渐近稳定性，给出了一类较为适用的积分判据，对它们的有效性和广泛性通过各种类型的例子作了说明．     

基于食饵保护的食饵-捕食捕鱼模型分析(英文)

In this paper,we consider a prey-predator fishery model with prey dispersal in a two-patch environment,one is assumed to be a free fishing zone and the other is a reserved zone where fishing and other extractive activities are prohibited.The existence of possible steady states of the system is discussed.The local and global stability analysis has been carried out.An optimal harvesting policy is given using Pontryagin s maximum principle.     

具时滞人机系统的稳定性与分支分析(英文)

A mathematical model of man-machine system is considered.Based on the reference [4],the direction and stability of the Hopf bifurcation are determined using the normal form method and the center manifold theory.Furthermore,the existence of Hopf-zero bifurcation is discussed.In the end,some numerical simulations are carried out to illustrate the results found.     

Hirota-Satsuma方程的N-孤子解(英文)

In this work,using the Hirota bilinear method,N-soliton solution is obtained for Hirota-Satsuma nonlinear evolution equation:u_t - u_xxt - 3u_xu_t + u_x = 0.     

多时滞线性切换系统的稳定性及其反馈镇定

研究了具有多时滞线性切换系统的稳定性及其反馈镇定问题,利用完备性条件、矩阵分解与二次Lyapunov泛函,给出了多时滞切换系统渐近稳定的充分条件和切换律设计方法.在此基础上,研究了这类系统的镇定控制问题,设计了保证系统时滞独立渐近镇定的控制器.     

一类周期线性时变切换系统的稳定性

讨论一类包含一组线性时变子系统和一个周期切换信号的切换系统的稳定性.在系统满足一定条件的情况下,利用Floquet定理,给出了周期线性时变切换系统指数稳定的充分必要条件.     

线性时变切换系统的渐近稳定性研究

考虑一类线性时变切换系统的渐近稳定性.基于矩阵测试理论,文中给出线性时变切换系统在周期切换和等时切换下渐近稳定的充分条件,并通过仿真实例说明结论是正确的.     

非线性离散开关系统的鲁棒镇定问题

利用切换Lypunov函数方法,把非线性离散开关系统的鲁棒镇定问题转化成一个矩阵不等式的最优解问题,给出了在任意切换下具有非线性扰动的线性开关系统的可鲁棒镇定的充分条件,并进一步讨论了同类时滞开关系统的鲁棒镇定问提.最后把以上结论推广到广义开关系统,由于结果均以矩阵不等式形式给出,便于验证和实现.     

一类切换线性系统的动态输出反馈H_∞控制:LMIs方法

研究一类由任意有限多个线性子系统组成的切换系统的动态输出反馈H∞控制问题.利用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换规则.采用消元法,将该矩阵不等式转化为一组线性矩阵不等式(LMIs).最后给出一个数值仿真实例证明结论的有效性.     

一类线性系统的数值控制设计

主要讨论了具有不稳定切换子模型的切换线性系统的稳定性问题.首先考虑了通过设计切换律来达到切换线性系统的稳定性问题.然后研究了切换线性控制系统可镇定性问题,通过设计控制律和切换律得到系统可镇定的判据.     

Estimation of Time Varying Linear Systems

Based on kernel and wavelet estimators of the evolutionary spectrum and cross-spectrum we propose nonlinear wavelet estimators of the time varying coefficients of a linear system, whose input and output are locally stationary processes, in the sense of Dahlhaus (1997). We obtain large sample properties of these estimators, present some simulated examples and derive results on the L ₂-risk for the wavelet threshold estimators, assuming that the coefficients belong to some smoothness class. This revised version was published online in June 2006 with corrections to the Cover Date.     

一类线性切换系统基于带有时滞观测器的输出反馈镇定

许多切换系统的状态是不可测或不能完全可测的,从观测器设计的角度重新考虑了带有时滞的线性切换系统的输出反馈镇定问题.主要研究了观测器带有延时,且控制器也带有切换延时的情况,最终得到了系统可镇定的充分条件.     

Stabilization of Stochastic Hybrid Linear Systems with Noise

Abstract

This article deals with the class of uncertain stochastic hybrid linear systems with noise. The uncertainties we are considering are of norm bounded type. The stochastic stabilization and robust stabilization problems are treated. Linear matrix inequality (LMI)-based sufficient conditions are developed to design the state feedback controller with constant gain that stochastically (robust stochastically) stabilizes the studied class of systems. Our results are mode independent and require only the complete access to the state vector. Numerical examples are given to show the effectiveness of the proposed results.     

基于LMIs的一类不确定线性切换系统的鲁棒控制

基于LMIs处理方法,研究了一类不确定线性切换系统在任意切换下的鲁棒控制问题.利用矩阵Schur补引理构造线性矩阵不等式,得到该系统的鲁棒稳定性的充要条件,同时也给出了在状态反馈下的鲁棒稳定性充要条件和在输出反馈下的充分条件.最后用数值例子对所得结果加以验证,说明了文中结果的正确性.