基于部分稳定性方法的离散时间多智能体系统的一致性

研究有向信息拓扑下离散时间线性多智能体系统的一致性分析与设计问题.利用提出的线性变换,将一致性问题转换为相应线性系统的部分变元渐近稳定性问题.基于部分变元稳定性理论,得到有向信息拓扑下离散时间线性多智能体系统达到渐近一致的基于矩阵Schur稳定性的充要条件和状态一致函数的解析表达式.同时设计了反馈增益矩阵.最后数值实例验证了所得理论的有效性.     

变时滞不确定奇异系统的输出反馈H_∞控制(英文)

针对同时含有变时滞和参数不确定性的奇异系统,研究了基于静态输出反馈的鲁棒H∞控制问题。采用Lya-punov泛函方法,给出了奇异系统时滞依赖渐近稳定且具有H∞范数界γ充分条件;利用含等式约束的线性矩阵不等式(LMI)方法,给出了此类系统存在输出反馈的时滞依赖充分条件,该条件等价于严格线性矩阵不等式可解性问题,利用严格LMI的可行解,得到控制器矩阵的参数化表示。与已有结果相比,此鲁棒控制器的渐近稳定性条件宽松,克服了时滞奇异系统稳定性问题条件中的等式约束。数值算例说明了该方法的有效性。     

离散时间多智能体系统一致性的平均驻留时间条件

研究高阶离散时间线性多智能体系统在有向切换信息拓扑下的状态一致性问题。首先通过提出的线性变换将该一致性问题转换为相应离散时间线性切换系统的渐近稳定性问题。然后借助于切换系统稳定性的平均驻留时间方法,分别得到如下两种情形下该一致性问题可解的充分条件：1)信息拓扑集合中的一部分拓扑是可一致的;2)信息拓扑集合中所有信息拓扑是可一致的。最后通过数值仿真验证了所得理论结果的正确性。     

基于T-S模糊模型的离散混沌系统变结构控制

研究了离散混沌系统模糊变结构控制问题.采用T-S模糊模型描述离散混沌系统,将离散混沌系统模糊化为局部线性模型.依据Lyapunov稳定性定理和线性系统变结构控制趋近律设计方法,设计了一种新型的离散变结构控制器,该控制器不仅能保证局部线性模型渐近稳定,而且能确保模糊动态模型全局渐近稳定.利用Matlab对确定Henon系统和不确定Henon系统进行数值仿真,结果表明所设计的控制器不但有效,而且具备很强的鲁棒性.     

线性离散时滞系统的输出反馈耗散控制

考虑线性离散时滞系统的二次型耗散控制问题,设计动态输出反馈使闭环系统渐近稳定且严格二次型耗散.先将系统严格二次型耗散性转化为线性矩阵不等式的可解性,得到了系统渐近稳定且严格二次型耗散的条件.然后讨论输出反馈耗散控制问题,给出了控制器的存在条件,总结出了控制器的综合方法、步骤.所得结果可为离散时滞系统的无源控制和H∞控制提供统一框架,也为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

一类参数不确定脉冲系统的保成本控制研究

根据脉冲系统的稳定性结果,得到了线性时变脉冲系统一致渐近稳定的充分条件．在此基础上研究了一类参数不确定系统的保成本状态反馈控制问题,根据稳定性理论与鲁棒控制原理得到了此类控制器的一个存在性条件．进一步通过有关参数不确定性的结论证明了该条件等价于一组线性矩阵不等式的可解性问题．最后给出了一个具体示例．     

逻辑型DES的稳定性

关于逻辑型离散事件系统 ,一致稳定性 ,一致可吸收性及一致渐近稳定性理论等已得到证明。这里则给出其稳定性 ,可吸收性及渐近稳定性的结论     

逻辑型DES的稳定性

关于逻辑型离散事件系统，一致稳定性，一致可吸收性及一致渐近稳定性理论等已得到证明。这里则给出其稳定性，可吸收性及渐近稳定性的结论。     

关于变系数线性微分方程的稳定性*

本文用矩阵测度和比较定量给出了变系数线性微分方程稳定性的一个简单判据，对周期系数的线性微分方程给出了较为精确的渐近稳定判据，推广和改进了文［１］的工作。     

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.     

离散广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是广义大系统理论的基本问题之一,对其稳定性的研究要比状态空间大系统复杂得多,因为广义大系统不仅需要考虑稳定性,而且还要考虑正则性和因果性(离散广义系统)及脉冲自由(连续广义系统).本文在所有孤立子系统都是正则的且具有因果关系的条件下,利用Lyapunov方程,应用Lyapunov函数方法,研究了广义离散线性大系统和广义离散非线性大系统的稳定性和不稳定性问题,给出了离散广义大系统稳定性和不稳定性判定定理,得到了离散广义大系统的关联稳定参数域和不稳定域.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

不确定离散奇异时滞系统的鲁棒稳定性

针对一类具有区间时变时滞和线性分式参数不确定性的离散奇异系统, 研究鲁棒稳定性问题。基于Lyapunov稳定性理论, 应用线性矩阵不等式方法, 给出不确定离散奇异时滞系统的新的时滞相关型稳定性准则。所给准则相比于已有一些结果, 包含较少的矩阵变量, 且具有较小的保守性。数值实例表明所得结果的有效性。     

AN LMI APPROACH TO ROBUST STABILITY OF UNCERTAIN DISCRETE SINGULAR TIME‐DELAY SYSTEMS

The problem of robust stability analysis for uncertain discrete singular time‐delay systems is investigated in this paper. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time‐delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncertain discrete singular time‐delay system. Two numerical examples are provided to demonstrate the feasibility of the proposed approach.     

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE‐TIME SINGULAR SYSTEMS WITH TIME‐DELAY AND NONLINEAR PERTURBATION

This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples.     

不确定离散广义系统因果性的鲁棒控制

讨论不确定离散广义系统的因果性鲁棒控制问题。对不改变原系统正则性的任意扰动,给出并证明了使闭环系统保持因果性的充要条件。最后举例证明了所给出的主要结果。     

Delay‐dependent robust stability and stabilization for uncertain discrete singular systems with delays

The robust stability and robust stabilization for time‐delay discrete singular systems with parameter uncertainties is discussed. A delay‐dependent linear matrix inequality (LMI) condition for the time‐delay discrete systems to be nonsingular and stable is given. Based on this condition and the restricted system equivalent transformation, the delay‐dependent LMI condition is proposed for the time‐delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilization are solved, and the delay‐dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the method given in the paper. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Stability and Stabilization Criteria for Discrete Singular Time‐Delay LPV Systems

This paper is concerned with establishing robust stability and stabilization criteria for discrete singular time‐delay linear parameter varying (LPV) systems. Firstly, a robust stability criterion is obtained for this class of systems by a delay‐partition approach, and thereby a less conservative sufficient condition which guarantees discrete singular time‐delay LPV systems to be admissible is given. Secondly, a class of state feedback controllers for stabilizing discrete singular time‐delay LPV systems is designed. Finally, compared with existing results, the numerical results of several examples illustrate the effectiveness of the approach proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Linear parameter-varying discrete time-delay systems: Stability and l 2-gain controllers

In this paper, we investigate a class of linear parameter-varying discrete time-delay (LPVDTD) systems where the state-space matrices depend on time-varying parameters and the delay is unknown but bounded. We treat both notions of quadratic stability based on a single quadratic Lyapunov function and affine quadratic stability using parameter-dependent Lyapunov functions. In both cases, we develop LMI-based results of stability testing for time-delay as well as delayless discrete-time systems. Then, we design state-feedback controllers which guarantee quadratic stability and an induced l ₂-norm bound. For the case of dynamic output feedback control, we use a parameter-independent quadratic Lyapunov-Krasovskii function to develop LMI-based solvability conditions which are evaluated at the extreme points of the admissible parameter set. Throughout the paper, complementary results for linear parameter-varying discrete (LPVD) systems without delay are presented.     

Jump modes analysis and observer design for discrete singular systems

This paper is concerned with the reconstructability and detectability of the jump modes of discrete singular systems. The notion of jump modes can be considered as the discrete counterpart of the impulsive modes of continuous singular systems which has been extensively studied. The effect of jump modes on the existence of reduced order normal Luenberger observers for discrete singular systems is investigated. Necessary and sufficient conditions for the existence of normal Luenberger observers and the corresponding observer design procedure are obtained.