具固定脉冲时刻的脉冲微分系统关于部分变元的指数稳定性

研究了具固定脉冲时刻的脉冲微分系统关于部分变元的指数稳定性,得到了保证零解关于部分变元指数稳定的充分条件,并给出了关于部分变元稳定性的一个新的判定准则.最后给出了其相关例子.     

部分稳定的李雅普诺夫函数与大系统的部分稳定性

随着科学技术的日新月异,近十年来,出现了规模庞大、结构复杂的大系统.例如,大型通讯、交通、电力、生态、化工、计算机、经济管理、人口控制等系统.其理论研究尚处于初创阶段.目前所见研究工作多是涉及大系统所有的状态变量.然而,实际上很多稳定性问题并不要求(或不可能要求)用同样方式处理所有变量.事实上,在某些问题中,我们感兴趣的只是某些状态变量的性状,或者实际上状态变量中只有某些可以使用,人们甚至不能得到其余状态变量的信息(这是由于不可去除的扰动造成的).因此,研究大系统对部分变元的稳定性是十分重要的.问题之一是:若每个孤立子系统对部分变元稳定(或不稳),当关联项满足什么条件,可以保证大系统对各子系统所涉及的部分变元都稳定(或     

离散大系统关于部分变元的关联稳定性

一、问题的提出在文献[1]中,曾提出了关于部分变元的稳定性问题.1957年,首先引进函数 V(t,x_1,…,x_n)关于变元 x_1,…,x_m(m≤n)为定号函数等概念,并给出了系统关于部分变元稳定性和渐近稳定性的定理.随后,许多学者从事这方面的研究工作.实际上这是与这个问题本身具有很重要的实用性分不开的.意义下的稳定性是针对系统的所有状态变量而言的.但实际上很多稳定性问题并不要求(或不可能要求)用同样的方式处理所有的状态变量.到目前为止,虽然关于全变元稳定性的许多结果已平行地推广到部分变元稳定性问题上来,但是从具体问题出发,来解决     

离散大系统关于部分变元的关联集合稳定性

本文利用Liapunov函数方法，研究了离散大系统关于部分变元的关联集合稳定性，给出了关于部分变元关联集合稳定性的几个基本定理的一些充分条件.     

离散大系统对部分变元的集合稳定性

本文讨论了离散系统对部分变元的集合稳定性。分别用标量Liapunov函数法和向量Liapunov函数法,给出了离散大系统对部分变元的集合稳定性的充分条件。考虑系统:     

离散大系统对部分变元的集合稳定性

本文讨论了离散系统对部分变元的集合稳定性。分别用标量Liapunov函数法和向量Liapunov函数法,给出了离散大系统对部分变元的集合稳定性的充分条件。考虑系统:     

一类具有多偏差变元的Liénard系统的反周期解

研究了一类具有多偏差变元的Liénard系统的反周期解,获得了该系统反周期解的存在性与全局指数稳定性的新充分条件.     

变系数线性系统谱的新不等式及其对部分变元稳定性的应用

本文利用一个非二次型李雅普诺夫函数,对变系数线性系统给出了一个新的谱不等式.不同于Wazewski不等式,我们避免了需要计算时变矩阵特征值的困难.然后我们利用新的谱不等式,讨论了变系数线性系统对部分变元的指数稳定性,得到了更实用的结果.     

线性周期系统的部分变元稳定性

本文对线性周期系统:x=A(t)x 的部分变元的稳定性问题进行了研究,得到了若干判别条件、证明了二次型 V—函数的存在性,同时也指出了它与其对应的离散系统的部分变元稳定性之间的关系的不等性。     

离散大系统关于部分变元的稳定性和有界性

本文利用文献[1—4]中大系统的分解理论及Lyapunov函数的加权,讨论了离散大系统关于部分变元的稳定性与有界性,得到了一些新的结果. 考虑由下列形式方程描述的离散时间系统:     

Partial exponential stability of nonlinear time-varying large-scale systems

In this paper, theorems concerning the partial exponential stability and globally partial exponential stability of nonlinear time-varying large-scale systems are obtained via both scalar and vector Lyapunov function methods and both scalar and vector comparison technique. By describing high-order systems as collections of lower interconnected subsystems so that the partial exponential stability and globally partial exponential stability property of isolated subsystems infers the same property of the over-all system, these theorems obtained here extend and complemented the relevant known results and enriched the contents of the partial exponential stability theory for nonlinear time-varying large-scale systems. Finally, two numerical examples are presented to illustrate the effectiveness of the results.     

Stability of switched systems with time delay

In this paper, we study the qualitative properties of linear and nonlinear delay switched systems which have stable and unstable subsystems. First, we prove some inequalities which lead to the switching laws that guarantee: (a) the global exponential stability to linear switched delay systems with stable and unstable subsystems; (b) the local exponential stability of nonlinear switched delay systems with stable and unstable subsystems. In addition, these switching laws indicate that if the total activation time ratio among the stable subsystems, unstable subsystems and time delay is larger than a certain number, the switched systems are exponentially stable for any switching signals under these laws. Some examples are given to illustrate the main results.     

Exponential stability and applications of switched positive linear impulsive systems with time-varying delays and all unstable subsystems

The global uniform exponential stability of switched positive linear impulsive systems with time-varying delays and all unstable subsystems is studied in this paper, which includes two types of distributed time-varying delays and discrete time-varying delays. Switching behaviors dominating the switched systems can be either stabilizing and destabilizing in the new designed switching sequence. We design new linear programming algorithm process to find the feasible ratio of stabilizing switching behaviors, which can be compensated by unstable subsystems, destabilizing switching behaviors, and impulses. Specically, we add a kind of nonnegative impulses which is consistent with the switching behaviors for the systems. Employing a multiple co-positive Lyapunov-Krasovskii functional, we present several new sufficient stability criteria and design new switching sequence. Then, we apply the obtained stability criteria to the exponential consensus of linear delayed multi-agent systems, and obtain the new exponential consensus criteria. Three simulations are provided to demonstrate the proposed stability criteria.     

Exponential stability of singularly perturbed switched systems with time delay

This paper investigates exponential stability of singularly perturbed switched systems with time delay. The multiple Lyapunov functions technique and dwell time approach are used to establish stability criteria for a switched system consisting of both stable and unstable subsystems. Examples are presented to illustrate the criteria.     

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.     

Uniform stability of switched nonlinear systems

In this paper, we investigate the stability properties of a general class of nonautonomous switched nonlinear systems. Sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are derived via multiple Lyapunov functions. Our results provide stability criteria for switched systems with both stable and unstable subsystems. Particularly, our results include some existing results as special cases or improve those in the literature. Several numerical examples are worked out to illustrate our results.     

灰色中立随机线性时滞系统的稳定性分析(英文)

通过使用灰色矩阵覆盖集的分解方法和矩阵范数的性质,构造李雅普诺夫函数,研究了灰色中立随机线性时滞系统的鲁棒稳定性和几乎指数鲁棒稳定性.     

Exponential stability of perturbed superstable systems in Hilbert spaces

We study exponential stability of superstable systems in Hilbert spaces under perturbations. Formulas to calculate or to estimate the exponential growth bound of the perturbed systems are derived via which sufficient conditions on exponential stability are established. The obtained results are applied to a partial differential equation governing the vibration of a smart beam made of self-straining material. Several numerical simulations are given.     

Robust exponential stability of switched delay interconnected systems under arbitrary switching

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories.     

Analysis and design of switched normal systems

In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.