一类Takagi-Sugeno模糊离散广义系统的稳定性判据

利用Lyapunov方法,研究了一类Takagi-Sugeno(T-S)模糊离散广义系统的稳定性问题．给出了该系统一致正则、因果和稳定的充分条件,并把此条件用线性矩阵不等式(LMI)表示．通过矩阵分解把广义系统的非严格矩阵不等式约束转化成严格的矩阵不等式约束,从而可以用LMI工具箱一次判定系统的稳定性,算例说明所给方法使用方便．     

离散广义系统稳定性分析与控制的Lyapunov方法

利用Lyapunov方法,研究离散广义系统稳定性分析与控制问题.得到了离散广义 系统正则、具有因果关系且渐近稳定的等价条件;还给出了相关的鲁棒稳定性分析与镇定方 法.     

不确定离散时滞广义系统的参数依赖稳定条件

研究了一类具有凸多面体不确定性的离散时滞广义系统的鲁棒稳定性问题。基于参数依赖的Lyapunov函数和线性矩阵不等式方法,推导出使系统正则、因果且鲁棒稳定的时滞相关型充分条件。算例验证了本文方法的可行性。     

离散广义系统的鲁棒稳定性

针对具有结构不确定性的离散广义系统,提出了一种新的鲁棒稳定性分析方法;得 到了使所考虑系统鲁棒稳定的条件,该条件保证对所有容许的结构摄动,离散广义系统正则、 因果且稳定;并进一步得到了所考虑系统具有鲁棒极点集的条件.     

离散广义区间动力系统的稳定性

利用范数理论,研究离散广义区间动力系统的稳定性问题,给出其区间动力系统的正则、因果且稳定的充分条件.在此基础上,进一步考虑该系统的区间极点集的配置问题,给出了使离散广义区间动力系统的极点落在预先给定园盘内的判定定理.数值算例表明了该方法的可行性.     

广义互联大系统的渐近稳定与分散镇定

利用Lyapunov函数方法、系统分解法以及矩阵不等式等方法研究一类具有脉冲行为的广义互联大系统的渐近稳定性及分散镇定问题,在子系统正则且零解渐近稳定的条件下,给出广义线性互联大系统的渐近稳定莉定的一个充分条件,并设计适当的反馈律,以实现广义互联大系统的镇定。通过仿真实例说明主要结果。     

离散广义T-S模糊系统的稳定性分析

针对广义模糊系统的结构特点和技术要求,构造出离散广义分段模糊Lyapunov函数的处理技术,讨论了输入采用双交叠模糊分化的离散广义T-S模糊系统的稳定性和控制器设计问题,在分段Lyapunov函数的基础上采用并行分布补偿法设计出离散广义模糊系统的模糊控制器,得出了新的判定闭环离散T-S模糊广义系统稳定性的充分条件,即在...     

广义系统具有正定解的Lyapunov方程

本文研究线性广义系统有正定解的Lyapunov方程，给出广义系统稳定等价于Lyapunov方程有正定解，进一步研究了广义系统R－能观，稳定和Lyapunov方程存在正定解三者之间的关系。基于该Lyapunov方程，给出广义系统允许（正则，稳定，无脉冲）的等价条件。     

离散滞后广义系统稳定域的定量估计

利用Lyapunov方法讨论离散滞后广义系统, 并给出了该类系统的零解一致稳定区域和渐近稳定区域的大小估计. 当初始扰动是在稳定区域时, 离散滞后广义系统的初始值问题的解一致稳定; 当初始扰动是在渐近稳定区域时, 离散滞后广义系统的初始值问题的解趋于零. 所举的仿真例子描述了该方法的应用.     

离散广义双线性系统的稳定控制

针对离散广义双线性系统,研究了稳定控制存在的条件,给出了相应的控制方案。所采用的方法是利用广义系统分解,选择适当的控制,运用Lyapunov方法证明线性状态控制可以使闹环系统在原点附近渐近稳定。对于这一类离散广义双线性系统有关理论的证明,可以看作是正常离散广义双线性系统的拓广。给出了一个可行性的应用算例,同时仿真结果也说明了该方法的有效性所得稳定性的判据对于选择合适的控制方案具有实际指导意义。     

2-D奇异线性离散系统渐近稳定性的一类Lyapunov 方法

引入2－D奇异一般离散状态空间模型的Lyapunov方程,探讨了该模型的渐近稳定性、特征多项式的根式以及2－D Lyapunov矩阵方程间的关系,给出了系统渐近稳定性的充分条件。     

具有滞后耦合特性的线性随机大系统的时滞无关均方稳定性*

本文研究具有滞后耦合特性的时不变线性Ｉｔｏ随机大系统的稳定性，得到了大系统平衡态滞后无关的均方渐近稳定性代数判据．文中所考虑的子系统是随机子系统，对它们的假设正好是它们均方渐近稳定的充要条件．另外，文中采用的Ｌｙａｐｕｎｏｖ泛函是确定型的Ｌｙａｐｕｎｏｖ泛函．     

Hybrid singular systems of differential equations

This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresponding dynamic systems is markedly different, our goals are to develop hybrid systems in which continuous dynamics are intertwined with discrete events under random-jump disturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markov chains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in the formulation. Under general assumptions, limit behavior of the underlying system is examined. Using weak convergence methods, it is shown that the systems can be approximated by limit systems in which the coefficients are averaged out with respect to the quasi-stationary distributions. Since the limit systems have fewer states, the complexity is much reduced.     

Asymptotic stability in probability and stabilization for a class of discrete‐time stochastic systems

This paper investigates asymptotic stability in probability and stabilization designs of discrete‐time stochastic systems with state‐dependent noise perturbations. Our work begins with a lemma on a special discrete‐time stochastic system for which almost all of its sample paths starting from a nonzero initial value will never reach the origin subsequently. This motivates us to deal with the asymptotic stability in probability of discrete‐time stochastic systems. A stochastic Lyapunov theorem on asymptotic stability in probability is proved by means of the convergence theorem of supermartingale. An example is given to show the difference between asymptotic stability in probability and almost surely asymptotic stability. Based on the stochastic Lyapunov theorem, the problem of asymptotic stabilization for discrete‐time stochastic control systems is considered. Some sufficient conditions are proposed and applied for constructing asymptotically stable feedback controllers. Copyright © 2014 John Wiley & Sons, Ltd.     

线性离散周期奇异系统的可解性与渐近稳定性

讨论了线性离散周期奇异系统初值问题的可解性和渐近稳定性问题.首先分析总结了线性离散变系数奇异系统可解性及其广义状态解的一般概念.在此基础上,定义了线性离散变系数奇异系统的一致渐近稳定性,并通过增加系统维数把线性离散周期奇异系统转化为线性定常奇异系统,从而得到了线性离散周期奇异系统可解和一致渐近稳定的充要条件.     

一类离散切换模糊系统的稳定性

针对离散模糊系统,提出一类离散切换模糊系统的稳定性问题.使用切换技术及单Lyapunov函数、多Lyapunov函数方法构造出连续状态反馈控制器,使得相应的闭环系统渐近稳定,同时设计可以实现系统全局渐近稳定的切换律.模型中的每个切换系统的子系统是离散模糊系统,取常用的平行分布补偿PDC控制器,主要条件以凸组合和矩阵不等式的形式给出,具有较强的可解性.计算机仿真结果表明设计方法的可行性与有效性.     

Asymptotic stability and instability of large-scale systems

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations. With minor technical adjustments, the theory is broadened to include considerations of unstable subsystems as well as instability of composite systems.     

Robust stability of homogeneous large-scale bilinear systems with time delays and uncertainties

This paper addresses the problem of stability analysis for homogeneous large-scale uncertain bilinear time-delay systems subjected to constrained inputs. Both nonlinear uncertainties and interval systems are discussed. Several delay-independent criteria are presented to guarantee the asymptotic stability of the overall systems. The main feature of the presented criteria is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equations that may be unsolvable. Three illustrative numerical examples are presented to verify the effectiveness of the proposed stability criteria.     

一种模糊系统稳定性的分析方法

针对T-S型模糊系统进行局部稳定性分析．首先指出模糊系统全局渐近稳定充分条件的不足，证明了此条件不是必要条件；然后将模糊集合的隶属度函数代入模糊系统表达式，得到一个特殊的非线性离散系统，从系统分析的区域、判定稳定的条件及稳定范围3方面确定稳定区域；最后对不稳定的系统给出了不稳定判据．仿真实例证明了这种方法的有效性．该方法对系统稳定点附近局部稳定性的判定有着很强的实用价值．