Kronecker指数等系统不变量与系统结构及参数的关系

1967年,D.G.Luenberger在推导标准形时,已接触到Kronecker指数,但不知其不变性. 1972年,V.M.Popov阐述并证明了Kronecker指数等系统不变量的不变性.本文讨论了这 些不变量与系统结构和参数的关系,阐明了这些不变量的物理意义,因之,也给了这些不变量 在一些变换下的不变性以明晰的物理解释.     

非线性随机时滞系统族的鲁棒稳定性

研究了不确定性的一族非线性随机时滞系统的指数稳定性,建立了这种系统的均 方指数稳定和几乎必然指数稳定的时滞相关的充分准则;然后应用这些充分条件到一类不确 定性的随机时滞神经网络,得到了这种神经网络指数稳定的实用判据.最后一个数值例子说 明所给准则的有效性.     

时滞切换不确定神经网络系统的指数稳定性

本文研究了具有无穷时滞切换不确定细胞神经网络(UCNNs)系统任意切换下的指数稳定性.利用同胚映射和M-矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用Lyapunov泛函方法,研究了时滞切换UCNNs系统任意切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.     

不校准视觉参数的非完整运动学系统的鲁棒指数镇定

基于视觉反馈和非完整（1,2）型移动机器人的标准链式形式,探讨了具有不校准视觉参数的机器人的鲁棒镇定问题,得到了这种机器人在图像平面内新的非完整运动学系统的不确定链式模型.借助于状态缩放和切换技术,对非完整不确定链式模型提出了新的指数镇定的时变反馈控制器,并给出了指数镇定的严格证明.仿真结果验证了控制器设计的有效性.     

非线性时变系统部分指数稳定的一次近似

通过非线性系统的线性化方法,讨论了一类非线性时变微分系统的解关于部分变量指数稳定的一次近似.利用齐次线性系统的Cauchy矩阵解、截断Cauchy矩阵解和Gronwall_Bellman不等式,得到了线性系统的解部分指数稳定确保原非线性系统的解局部部分指数稳定的充分条件,其中一些结果可以保证部分变量有不同的指数收敛率.最后给出了一些实例说明了所用方法的有效性.     

一类随机人口发展系统的指数稳定性

对人口系统的讨论 ,通常的数学模型没有考虑外界环境对系统的影响 .在假设随机的外界环境对迁移产生扰动的条件下 ,给出Hilbert空间中一类随机时变人口发展系统 .对随机时变人口发展系统的均方稳定性和指数稳定性进行了讨论 .利用Burkholder_Davis_Gundy不等式 ,Gronwall引理和Kolmogorov不等式得到了均方稳定和指数稳定的充分条件 .最后提出如果生育率选作控制变量 ,系统仍然是均方和指数稳定的 ,并可进一步讨论它的最优控制问题     

不确定变时滞随机系统的鲁棒均方指数稳定性

研究了不确定变时滞随机系统的鲁棒均方指数稳定性问题, 不确定性是范数有界的. 通过构造Lyapunov泛函, 得到了基于线性矩阵不等式的鲁棒均方指数稳定的充分条件. 最后给出实例加以验证所提出方法的有效性.     

不确定广义跳变时滞系统的鲁棒指数稳定性

讨论不确定广义跳变时滞系统的鲁棒指数稳定性问题. 利用线性矩阵不等式(LMI)技术给出一个时滞区间依赖条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 数值例子说明本文的结果改进了已有的结论.     

不确定切换奇异时滞系统鲁棒指数容许性分析

讨论一类连续时间不确定切换奇异区间时变时滞系统的鲁棒指数容许性问题. 通过定义衰减率依赖李亚普诺夫函数并利用平均驻留时间法, 给出一个时滞区间依赖充分条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 本文获得的结论为连续时间切换奇异时滞系统的基本问题提供了一个解, 即识别切换信号使得切换奇异时滞系统正则、无脉冲且均方指数稳定. 数值例子说明本文结果的有效性.     

具有拓扑切换特性的离散型不确定时空网络的指数同步

研究了具有拓扑切换特性的离散型不确定时空网络的指数同步问题. 基于稳定性理论, 构造了具有指数形式的Lyapunov函数, 并设计了同步控制器的结构方程, 进而获得了时空网络的同步条件. 同时, 我们设计了未知参数的识别律, 有效地识别了网络中的未知参数. 最后, 选取实际的激光相位共轭波空间扩展系统作为网络节点进行仿真模拟, 验证了同步方案的可行性与控制器的有效性. 通过构造具有指数形式的Lyapunov函数, 能够有效地调节网络的同步速率. 并且获得的同步条件中不包含网络的耦合矩阵项, 消除了拓扑切换特性对同步过程的影响, 使得网络同步性能更加稳定.     

Stability analysis of hybrid switched nonlinear singular time-delay systems with stable and unstable subsystems

The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.     

Analysis of robust stability for switched systems with multiple time-delays

The sufficient conditions of delay-dependent exponential stability for switched systems and robust exponential stability for uncertain switched systems with two time-delays are presented by using average dwell time method and free-weighting matrix method.The interaction between different time-delays is considered.The sufficient conditions do not need that every subsystem is stable.The designed methods of the switching law are also given.The sufficient conditions are given in the form of linear matrix inequalities that can be solved easily.The result is proven to be valid by the simulation at last.     

滞后动态系统广义指数稳定的充要条件

本语文针对一般的滞后动态系统建立了广义指数稳定性的充分和必要条件，并由所建立的充要条件得出了系统过渡过程的时变指数衰减估计，作为所建结果的应用，基于矩阵工给出了一类滞后动态系统过渡过程的相应指数衰减估计，本文揭示了所建衰减估计可好于那些仅基于充分稳定性条件所得的估计。     

变时滞神经网络指数同步性的LMI新条件

研究了一类具有变时滞的非线性混沌神经网络的指数同步性问题。应用线性矩阵不等式和Lyapunov泛函方法,得到了具有驱动-响应结构的神经网络的指数同步性准则,建立了判断神经网络同步性的新的充分条件。通过实例说明了该方法的可行性和有效性。     

New results on robust exponential stability of integral delay systems

The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov–Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.     

Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function

In this paper, the problem of exponential stability and stabilization for a class of uncertain linear time-varying systems is considered. The system matrix belongs to a polytope and the time-varying parameter as well as its time derivative are bounded. Based on a time-varying version of Lyapunov stability theorem, new sufficient conditions for the exponential stability and stabilization via parameter dependent state feedback controllers (i.e., a gain scheduling controllers) are given. Using parameter dependent Lyapunov function, the conditions are formulated in terms of two linear matrix inequalities without introducing extra useless decision variables and hence are simply verified. The results are illustrated by numerical examples.     

Stability analysis of dynamical neural networks

In this paper, we use the matrix measure technique to study the stability of dynamical neural networks. Testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given. It shows how a few well-known results can be unified and generalized in a straightforward way. Local exponential stability of a class of dynamical neural networks is also studied; we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks are obtained     

时滞分布参数控制系统指数镇定的LMI方法

A renovating method for distributed parameter control systems with constants, varying-delays, and multi-varying-delays is put forward. By constructing average Lyapunov functions and employing linear matrix inequality (LMI) and other matrix inequality technologies, several sufficient conditions for exponential stabilization are derived. In this method, the conditions are delay-dependent and at the same time, the upper-bound of exponential convergence rate is obtained. In addition, the distinctive advantage of our method is that the criteria mentioned in the paper are easy to check, so it can be applied to practice easily. Finally, a computation example is given to illustrate the proposed method.     

Improved exponential estimates for neutral systems

Improved exponential estimates and a new sufficient condition for the exponential stability of neutral type time‐delay systems are established in terms of linear matrix inequalities (LMIs). A new Lyapunov‐Krasovskii functional candidate with appropriately constructed exponential terms is introduced to prove the exponential stability and to reduce the conservatism. For the uncertain case, a corresponding condition for the robust exponential stability is also given. It is shown by numerical examples that the proposed conditions are less conservative than existing results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Global Exponential Stability Analysis of Discrete‐Time Genetic Regulatory Networks with Time Delays

This paper focuses on the study of global robust exponential stability of discrete‐time genetic regulatory networks (GRNs) with time‐invariant/time‐varying delays and parameter uncertainties. Many existing results on this problem are based on the linear matrix inequality (LMI) approach, which needs to verify whether there exists a feasible solution of a set of LMIs. Along with the increase in the number of genes, dimensions of LMIs will increase accordingly, which will lead to a large amount of calculation. Based on M‐matrix theory, sufficient conditions ensuring the global robust exponential stability of a class of discrete‐time GRNs with time‐invariant/time‐varying delays and parameter uncertainties are presented. These given conditions are to check whether a constructed constant matrix is a nonsingular M‐matrix. Simulation results of several examples are given to demonstrate the validity of the proposed method.