关于一类脉冲切换系统的鲁棒H∞控制

研究一类具有扰动的脉冲切换线性系统的鲁棒H控制问题.分别从系统的鲁棒稳定性及其鲁棒性能两方面进行分析.首先利用Lyapunov函数法对系统的稳定性进行分析,给出了系统鲁棒渐近稳定的几个重要的充分条件,通过它很容易判断系统是否鲁棒稳定.进一步运用线性矩阵不等式(LMI)法对系统鲁棒性能进行分析,得到了一般系统的状态反馈矩阵和脉冲控制矩阵,并在此基础上得出了一个鲁棒H控制律.最后提出了一套基于MAT-LAB软件的鲁棒控制器的设计方法,并通过一个数值例子很好地验证了文中主要结论的有效性.     

一类脉冲随机混杂系统的鲁棒H无穷控制

本文研究具有外在扰动的脉冲Markov切换线性随机系统的鲁棒H无穷控制问题,分别从系统的鲁棒稳定性及鲁棒性能两方面进行分析,首先,利用多Lyapunov函数法对系统的稳定性进行分析,给出了系统鲁棒依概率稳定的充分条件,进一步,运用线性矩阵不等式(LMI)法对系统的鲁棒性能进行分析,给出相应的状态反馈增益矩阵和脉冲控制增益矩阵的求解方法,在此基础上得出了一个鲁棒H无穷控制律,并提出了一套基于Matlab软件的鲁棒控制器的设计方法。最后,数值算例说明所设计方法的有效性。     

一类脉冲随机混杂系统的鲁棒H∞控制

研究了具有外在扰动的脉冲Markov切换线性随机系统的鲁棒H∞控制问题,分别从系统的鲁棒稳定性及鲁棒性能两方面进行分析:首先,利用多Lyapunov函数法对系统的稳定性进行分析,给出了系统鲁棒依概率稳定的充分条件;进一步地,运用线性矩阵不等式(LMI)法对系统的鲁棒性能进行分析,给出相应的状态反馈增益矩阵和脉冲控制增益矩阵的求解方法.在此基础上得出了一个鲁棒H∞控制律,并提出了一套基于MATLAB软件的鲁棒控制器的设计方法.最后,利用数值算例说明所设计方法的有效性.     

区间离散Lurie系统的绝对稳定性

用Lyapunov函数研究了具有单调扇形限制的多非线性项的区间离散Lurie系统的鲁棒绝对稳定性, 给出了此类区间离散Lurie系统的鲁棒绝对稳定性的矩阵不等式形式的代数判据, 并与区间对称矩阵稳定性建立了联系.     

不确定多重状态时滞离散系统的LMI鲁棒稳定条件

研究了具有多重状态时滞的凸多面体不确定离散系统的鲁棒稳定性分析问题．基于参数依赖的李亚普诺夫稳定性和线性矩阵不等式推导出使得时滞鲁棒稳定系统鲁棒稳定的充分条件．应用此条件，通过测试一组线性矩阵不等式的可解性即可达到判定系统的鲁棒稳定性的目的．因为使用了参数依赖的李亚普诺夫稳定性思想，此鲁棒稳定条件比基于二次稳定概念的稳定条件的保守性更小．算例验证了结果．     

广义不确定周期时变系统的鲁棒稳定性分析

研究广义不确定周期时变系统的鲁棒稳定性问题.基于广义周期时变系统Lyapunov不等式,提出了广义不确定周期时变系统鲁棒稳定的概念,采用矩阵不等式(LMI)方法,得到了该类系统鲁棒稳定的充分必要条件;然后,进一步研究了在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法;最后,引入了广义周期时变系统二次稳定的概念,并讨论了二次稳定性与鲁棒稳定性之间的关系.     

鲁棒稳定性和鲁棒对角优势的关系

本文研究了多输入多输出系统的鲁棒稳定性和鲁棒对角优势的关系.不仅给出了使系统 鲁棒对角优势所需的鲁棒稳定性条件,而且还得出了系统鲁棒对角优势一定保证系统鲁棒稳 定这个一般性的结论.并可根据本文所给的结果,对允许摄动的最大边界进行估计,包括非结 构摄动的范数上界和结构性摄动的摄动矩阵的各元素的模的估计.本文得出的鲁棒对角优势 保证鲁棒稳定的结果是较少保守性的.     

切换系统的鲁棒二次公共Lyapunov函数矩阵寻找算法

为了获得不确定线性切换系统稳定性判别的公共二次Lyapunov函数寻找方法,提出了鲁棒公共二次Lyapunov函数的概念,运用矩阵不等式分析,得到了在鲁棒稳定矩阵集对合和不对合的情况下,鲁棒公共二次Lyapunov函数存在的充分性条件以及LMI形式的递推搜寻算法。获得的结果便于计算机实现,对不确定切换系统鲁棒稳定性判别具有一定价值。应用仿真测试验证了其正确性。     

带有时滞的区间动力系统的鲁棒稳定性研究

给出了区间动力系统稳定性的相关概念,讨论了带有时滞的区间动力系统的鲁棒稳定性.通过构造控制矩阵和迭代相结合的方法,给出了一类带有时滞的区间动力系统鲁棒稳定的判别方法,并且给出了系统鲁棒稳定时参数取值的最大区间.将含有时滞的区间动力系统的稳定性转化为判别一个矩阵的稳定性,推广和改进了已有的结论.     

具有输入时滞的不确定采样系统的鲁棒控制

针对具有输入时滞的结构不确定采样系统,研究了该类系统基于离散化模型的鲁棒控制器设计问题。通过将采样系统的连续的结构不确定对象离散化得到其近似模型,使具有输入时滞不确定采样系统的鲁棒控制器设计问题转换为讨论具有输入时滞的离散系统的鲁棒稳定性问题。利用Lyapunov函数的构造及解析技巧,给出了基于线性矩阵不等式(LMI)的输入时滞离散系统的鲁棒稳定性条件,并在此基础上将控制器参数化,得到了一个通过求解线性矩阵不等式(LMI)来获得采样系统鲁棒控制器的设计方法,所设计的控制器保证了系统的鲁棒稳定性,对结构摄动有着较好的鲁棒性能。最后,通过数值计算仿真验证了本文方法的可行性。     

一类具有非线性不确定性的时滞系统鲁棒控制

研究一类具有非线性不确定参数以及状态滞后线性系统的时滞依赖鲁棒稳定性判据和鲁棒镇定问题。提出了新的鲁棒可镇定判据和相应的鲁棒无记忆状态反馈控制器设计方法,导出的时滞依赖结果以线性矩阵不等式的形式给出。     

Criteria for robust absolute stability of time-varying nonlinear continuous-time systems

The present paper establishes results for the robust absolute stability of a class of nonlinear continuous-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov Second Method, criteria for robust absolute stability are obtained in different forms for the given class of systems. Specifically, the parametric classes of Lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability. The piecewise linear Lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations. Several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases. Two examples are presented as applications of the present results to a particular second-order system and to a specific class of systems with time-varying interval matrices in the linear part.     

Robust stability of impulsive Takagi-Sugeno fuzzy systems with parametric uncertainties

This paper presents a kind of time-varying impulsive Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties in which each subsystem of the model is time-varying. Several robust stabilities of time-varying systems with parametric uncertainties, such as general robust stability, robustly asymptotical stability and exponential stability, are studied using uniformly positive definite matrix functions and the Lyapunov method. Specifically, robust stability conditions of time-invariant impulsive T-S fuzzy systems are also derived in the formulation of quasi-linear matrix inequalities (QLMIs) and an iterative LMIs algorithm is designed for solving QLMIs. Finally, a unified chaotic system with continuous periodic switch and a unified time-invariant chaotic system are used for demonstrating the effectiveness of our respective results.     

不确定广义线性时变系统的鲁棒稳定和二次稳定

针对不确定广义线性时变系统,采用矩阵不等式的分析方法,提出不确定广义线性时变系统鲁棒稳定和二次稳定的概念.建立该类系统的矩阵不等式,将该类系统的鲁棒控制问题转化为求解矩阵不等式问题,得到该类系统鲁棒稳定和二次稳定的充分必要条件,并给出一种状态反馈鲁棒镇定控制器的设计方法.最后,通过数值算例表明了所提出方法的可行性.     

多智能体系统实现鲁棒一致的时延相关稳定判据

考虑存在多个时变时延、有限能量扰动以及时变拓扑结构不确定等网络约束条件,给出了多智能体系统实现鲁棒一致性的时延相关稳定判据.首先,利用状态分解将原问题转化为讨论不一致向量系统的鲁棒稳定性;然后,考虑到多个时变时延和动态拓扑,采用构造Lyapunov-Krasovskii泛函的方式分析系统鲁棒稳定性,并利用自由权矩阵方法获得关于非线性矩阵不等式(NLMI)的可行解判据;最后,借鉴求解锥补问题的思想,对NLMI判据进行非线性最小化处理,以得到保守性低、易于求解的LMI稳定判据.数值实例和仿真结果均验证了所提出判据的有效性.     

Robust stability analysis of time-varying systems using time-varying quadratic forms

We consider the robust stability of time-varying linear systems subject to structured time-varying uncertainty. We provide an alternate proof of the result that robust stability holds if and only if a scaled small-gain condition holds asymptotically. The new proof employs an extension of the so-called S-procedure losslessness theorem to time-varying quadratic forms which is of independent interest.     

Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses

In this paper, the robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses is considered. It is assumed that the considered impulsive neural networks have norm-bounded parametric uncertainties and time-varying delays and the state variables on the impulses may relate to the time-varying delays. By using Lyapunov functions together with Razumikhin technique or with differential inequalities, some new robust exponential stability criteria are provided. Some examples and their simulations, including examples that the stability of which can not be tackled by the existing results, are also presented to illustrate the effectiveness and the advantage of the obtained results.     

Tube-based robust MPC for linear time-varying systems with bounded disturbances

In this paper, a novel synthesis approach for tube-based robust MPC is proposed. A novel feature is the fact that the proposed tube-based robust MPC algorithm can deal with both time-varying parameter and bounded disturbance. The proposed control law is the linear combination of two components. The first component steers the state of the nominal linear time-varying system to the origin. The second component keeps the state at each time step of the linear time-varying system with bounded disturbance within a tube whose center is the state of the nominal linear time-varying system. Finally, the state of the linear time-varying system with bounded disturbance is kept within a tube whose center is at the origin so robust stability is guaranteed. Satisfaction of the state and control constraints is ensured by employing tighter constraint sets for the nominal linear time-varying system. The computational burdens are the same as those in the case of the nominal linear time-varying system.     

Robust stability and robust pole assignment of linear systems withstructured uncertainty

Sufficient conditions for the robust stability of linear time-varying systems are presented. The stability criteria are extended to the problem of the robust pole assignment of linear time-invariant systems to a specified region. These criteria, both for robust stability and robust pole assignment, improve some results in the literature. Examples are given to demonstrate the new criteria