控制饱和离散时滞线性系统的渐近稳定性

研究了饱和控制多输入离散时滞线性系统的稳定性问题．在满足一定的假设条件下,针对执行器出现饱和控制的情况,通过定义多输入饱和度函数,基于Lyapunov方法给出系统全局渐近稳定的充分性判据,并在系统不满足所给判据时给出其不变吸引域的描述．最后,设计一个算法来实现所得结果,并通过数值算例验证算法的可行性与有效性．     

一类相异功能反应的predator-prey扩散系统的稳定性

针对斑块生境下具有庇护所效应的相异功能性反应predator-prey扩散系统,讨论了系统持续生存的条件.运用常微分方程定性理论讨论了系统解的有界性,通过构造Lyapunov函数得到了一定条件下该系统正解是全局渐近稳定的.进一步利用Pioncare定理和Brower定理证明了惟一周期正解的存在性与稳定性.     

离散线性循环切换时滞系统驻留时间的确定

研究了一类在循环切换律下,子系统含有状态时滞的离散时间线性切换系统的稳定性和子系统驻留时间确定的问题.通过在每个子系统上建立Lyapunov函数,采用多Lyapunov函数方法,并基于线性矩阵不等式技术,得到系统渐进稳定的充分性条件,进而根据稳定性条件对每个子系统驻留时间的约束,得出计算子系统可行驻留时间值的数值搜索算法,仿真算例验证了算法的有效性.     

状态饱和非线性离散时滞系统的渐近稳定性

研究具有状态饱和非线性的离散多时滞不确定系统的鲁棒渐近稳定性,其中时滞为有界时变函数且不确定性满足范数有界条件．利用离散Lyapunov稳定性理论,结合矩阵不等式方法,获得了系统全局鲁棒渐近稳定的时滞相关充分条件．进一步给出了当系统具有定常时滞、单时滞和无时滞以及无不确定性时的渐近稳定条件,将所得结果与已有研究结果进行比较说明．最后,通过数值算例验证了所得结果的可行性．     

基于观测器的一类离散非线性系统的控制

研究一类离散非线性系统的观测器设计问题,基于Schur补引理和Lyapunov稳定性定理,提出一类离散非线性系统的观测器设计方法.证明了在适当条件下,提出的观测器保证观测误差渐近趋于零.进一步,提出了基于观测器一类离散非线性系统的反馈控制器设计方法.并给出在反馈控制的作用下相应闭环系统达到稳定的充分条件.     

多时滞反应扩散Cohen-Grossberg神经网络的稳定性

研究了一类具有反应扩散项的时滞Cohen—Grossberg神经网络模型利用拓扑度理论和Lyapunov函数方法，研究了此类系统平衡点的存在性及全局指数稳定性，给出了判定定理．     

具有Beddington-DeAngelis功能性反应的三维顺环捕食系统

利用常微分方程的比较定理,得到系统一致持续生存的充分条件,使用Brower不动点定理和Lyapunov函数,证明了周期系统在一定条件下,存在唯一的全局渐近稳定的正周期解,进一步讨论了概周期现象,并得到了概周期系统存在唯一的全局渐近稳定的概周期正解的充分条件,最后给出了周期系统的数值模拟,验证了理论结果的正确性.     

含有微分代数子系统的混杂系统稳定性研究

针对目前广泛存在的微分代数混杂系统(DAHS)的一般模型,提出了包括稳定性和(大范围)渐近稳定性概念的稳定性理论框架.利用单李雅普诺夫(Lyapunov)函数和多李雅普诺夫函数工具,得出了在任意切换及慢切换条件下判断DAHS的稳定性及渐近稳定性的充分条件.尤其对仅包含线性微分代数子系统的混杂系统,还具体给出了其切换序列的选择办法,以使整个系统达到大范围渐近稳定.在一个包括两个线性微分代数子系统的DAHS实例中,用相关定理得出了切换序列的选择办法,使得整个系统稳定.     

不确定时滞离散模糊系统鲁棒H∞控制

研究了一类不确定离散时滞模糊系统的鲁棒H_∞稳定性问题．基于模糊Lyapunov-Krasovskii函数,应用并行分布补偿算法,设计了使模糊系统全局渐近稳定的控制器,提出并证明了一个新的判别闭环不确定离散时滞模糊系统鲁棒H_∞渐近稳定的充分条件．引入多个附加矩阵变量,可由一组线性矩阵不等式的解得到控制器．由于使用了模糊Lyapunov-Krasovskii函数,此鲁棒稳定条件比基于公共Lyapunov-Krasovskii函数的稳定条件的保守性更小,由仿真算例验证了结果．     

一类时滞离散模糊系统的H∞性能分析

研究了一类不确定时滞离散模糊系统鲁棒H∞控制问题．基于模糊Lyapunov—Krasovekli函数,应用并行部分补偿算法,设计了使模糊系统全局渐近稳定的控制器,提出并证明了一个新的判别闭环一类离散时滞模糊系统H∞渐近稳定的充分条件．     

Consensus and formation control of discrete-time multi-agent systems

Consensus problems for discrete-time multi-agent systems were focused on.In order to design effective consensus protocols,which were aimed at ensuring that the concerned states of agents converged to a common value,a new consensus protocol for general discrete-time multi-agent system was proposed based on Lyapunov stability theory.For discrete-time multi-agent systems with desired trajectory,trajectory tracking and formation control problems were studied.The main idea of trajectory tracking problems was to ...     

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.     

离散时间PWS的分段广义H2动态输出反馈控制

基于分段二次李雅普诺夫函数．对离散时间分段系统提出了广义H2稳定控制器的设计方法．通过构造分段动态输出反馈控制器。使闭环系统广义H2全局稳定．利用线性矩阵不等式理论。给出了闭环系统广义H2全局稳定的一个充分条件．     

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     

最小事件间隔时间可设计的分布式事件触发优化算法

针对多智能体系统中的分布式凸优化问题,本文提出一种基于自适应事件触发机制的零梯度和优化算法.基于虚拟时钟设计了一种自适应事件触发条件,当每个智能体的虚拟时钟满足该条件时才触发条件,有效地降低了控制器的更新次数和系统的通信负担.通过构造李雅普诺夫函数,证明了在该算法下所有智能体的状态能渐近收敛到全局最优解.此外,所设计的事件触发条件使得最小事件触发间隔时间可设计,有效地排除Zeno行为.最后,通过仿真验证了该算法的有效性.     

一种基于动态事件触发的分布式优化算法

针对多智能体系统优化问题,提出一种基于动态事件触发机制的分布式优化算法.基于李雅普诺夫函数方法设计一种新型的动态事件触发控制器,相较于传统静态事件触发控制方法,所提出算法可有效降低多智能体间通信负担以及控制器计算负担.此外,利用周期采样信息进行事件触发条件设计,可避免智能体连续检测事件触发条件,并可消除Zeno现象.通过数值仿真验证了算法的有效性.     

Delay-independent decentralized H∞ control for multi-channel discrete-time systems with uncertainties

A robust decentralized H∞ control problem was considered for uncertain multi-channel discrete-time systems with time-delay. The uncertainties were assumed to be time-invariant, norm-bounded, and exist in the system, the time-delay and the output matrices. Dynamic output feedback was focused on. A sufficient condition for the multi-channel uncertain discrete time-delay system to be robustly stabilizable with a specified disturbance attenuation level was derived based on the theorem of Lyapunov stability theory. By setting the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller, the problem was reduced to a linear matrix inequality (LMI) which is sufficient to existence condition but much more tractable. An example was given to show the efficiency of this method.     

Robust stability for the perturbed sampled-data systems

Recently, efforts have been directed towards theproblem of robust stability, and consequently robuststabilization. A wealth of results has been accumulatedeither in frequency-domain or time-domain for continu-ous-time and discrete-time. In both cases unstructuredand/or structured parameter perturbations were consid-ered and robust stability measures were derived. Thesemeasures are quite conservative, but provide a good a-nalysis and design tools.By means of the second method of Lyapunov, this…