广议周期时变系统的允许性分析

研究了广义周期时变系统的允许性问题.通过研究背景的介绍，给出了系统允许的概念；建立了Lyapunov不等式，把系统的允许性问题转化为Lyapunov不等式的数值解问题，并利用矩阵不等式方法进一步讨论了系统的允许性，得到了系统允许的充分必要条件和两个推论.最后通过数值算例说明了所得出的主要结果.     

一般广义不确定周期时变系统的鲁棒稳定性

针对一般广义不确定周期时变系统存在鲁棒稳定性问题,根据一般广义周期时变系统的Lyapunov不等式,提出一般广义不确定周期时变系统鲁棒稳定的概念,并采用矩阵不等式（LMI）方法进行分析,得到了该类系统鲁棒稳定的充分必要条件.研究了在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一组状态反馈鲁棒控制器的设计方法;引入了一般广义不确定周期时变系统二次稳定的概念,讨论了二次稳定性与鲁棒稳定性的关系,是广义定常系统相应结论向一般广义周期系统的自然推广.     

一类广义混杂系统的随机稳定性及稳定化

针对切换序列为齐次有限状态Markov链的离散广义混杂系统,采用多Lyapunov函数和随机广义Lyapunov函数相结合的方法,无需对广义系统作受限等价变换,得到了系统随机稳定的充要条件,该条件以耦合广义Lyapunov方程(Coupled Generalized Lyapunov Equation,缩写CGLEs)的形式给出,可化为严格线性矩阵不等式(SLMIs)来进行求解．然后,进一步对系统的稳定化问题进行了分析与设计,给出了状态反馈增益矩阵的求解方法．最后的数值算例说明了该方法的有效性．     

广义不确定周期时变系统的鲁棒容错H_∞控制

针对一类广义不确定周期时变系统,利用线性矩阵不等式和李雅普诺夫不等式的分析方法提出了广义不确定周期时变系统的鲁棒二次稳定和鲁棒二次可镇定且具有H∞性能指标的概念.得到了该类系统鲁棒容错H∞控制的充要条件,研究成果是广义不确定定常系统鲁棒容错H∞控制结论向广义不确定周期时变系统的推广,因而具有较大的理论意义.最后,使用一个数值算例证明了该方法和结论的有效性.     

离散广义系统的正实性分析

目的研究离散广义系统严格正实分析和控制问题．方法使用分块矩阵、等价变换等代数方法，证明了离散广义系统严格正实的充分必要条件．结果得出了等价情形的新正实定理．结论为寻找用简单方法通过线性矩阵不等式（LMI）构造正实反馈控制器，进一步处理非正实系统实现问题奠定了理论基础．     

一类不确定奇异系统的鲁棒控制

研究一类不确定奇异系统的广义二次可稳性问题,给出此类不确定奇异系统广义二次稳定及广义二次可稳的概念,通过构造线性矩阵不等式,并利用矩阵Schur补引理,获得了此类不确定奇异系统广义二次可稳的充分必要条件,同时提出了闭环系统状态反馈控制律的设计方法,并用数值算例验证了该方法的有效性.     

含一般时延的高阶泛函微分方程的周期解

研究了一类含有"一般"时延的高阶泛函微分方程的周期解问题,将原方程化为等价的泛函微分方程,并利用该等价泛函微分方程的特征方程,得到了原方程具有周期解的充分必要条件,即其等价方程的特征方程具有不为零的纯虚根。     

线性时变系统的若干问题

线性时变系统由于状态转移矩阵的特性一般不能由系统矩阵的Ａ（ｔ）的特下值来表征,确定时变系统的稳定性是十分困难的。讨论了线性时变系统能控性的两个必要条件及其能稳定性的一个充分条件。     

动态投入产出系统结构稳定的充要条件

给出了经济领域内广义系统的结构稳定性的定义,研究了广义系统的结构稳定性问题,利用稳定性理论给出并证明了一般广义系统、动态投入产出系统结构稳定的充分必要条件.     

一类具有Ivlev型功能反应的L-V扩散系统的周期解

对一类具有Ivlev功能反应的扩散系统进行了研究,得到了系统能够持久生存的充分依据。同时系统是周期系统时,通过构造Lyapunov函数得到了系统存在全局渐近稳定的周期解,最后利用MATLAB软件对上述结论进行了数值模拟。     

Robust reliable H_∞ control for a class of uncertain time-delay systems

This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time-varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a linear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.     

广义线性系统容许的新判据

证明了广义线性系统的容许性可用单一的严格线性矩阵不等式形式来表示,得到了判断广义线性系统是否容许的新的充要条件,这一形式较先前给出的形式更便于应用LMI工具箱来判断广义线性系统的容许性,数值算例说明方法的可行性。     

Robust stability of discrete-time nonlinear system with time-delay

The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.     

Decentralized H∞ state feedback control for large-scale interconnected uncertain systems with multiple delays

Decentralized H∞ control was studied for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. A sufficient condition which makes the closed--loop system decentralized asymptotically stable with H∞ performance was derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities. The method overcomes the limitations of the existing algebraic Riccati equation method. Finally, a numerical example was given to demonstrate the design procedure for the decentralized H∞ state feedback controller.     

Robust stability of discrete-time nonlinear system with time-delay

The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities. Foundation item: Project (60425310) supported by the National Natural Science Foundation of China; project (2001AA4422200) supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China     

基于观测器的线性中立时滞系统控制

针对确定性中立时滞系统,利用Lyapunov函数法研究了该系统基于观测器的控制问题。结合线性矩阵不等式(LM I)方法,给出了该系统基于观测器渐近稳定的充分条件及观测器控制律的设计方法。最后的仿真例子说明了所给方法的有效性和可行性。     

带有非线性扰动的不确定奇异时滞系统的保性能控制

针对一类带有非线性扰动的不确定奇异时滞系统,基于Lyapunov稳定性理论和线性矩阵不等式处理方法,给出系统鲁棒保性能状态反馈控制器存在的充分条件和设计方法.所设计的保性能控制器保证了对所有容许的不确定性,不仅使得相应的闭环系统达到二次稳定,同时保证闭环性能指标函数具有上界.最后,通过仿真实例说明了所给方法的有效性.