具有时滞的线性区间动力系统的鲁棒稳定性

利用Lyapunov原理,给出了具有时滞的线性区间动力系统鲁棒稳定的一些充分条件,推广和改进了前人关于具有时滞的线性区间动力系统的鲁棒稳定性的相关结论,并举例说明了本文结果不仅保守性小,且计算简单.     

一类非线性广义系统的时滞相关耗散控制

针对一类带有非线性摄动的广义时滞系统,研究了时滞相关的鲁棒耗散问题.讨论了此类非线性广义时滞系统的鲁棒耗散性.同时对此类非线性广义时滞系统的二次稳定性进行了研究,分别用线性矩阵不等式（LMI）的方法给出了充分条件,也给出了时滞相关的鲁棒耗散的时滞上界.并且,给出了时滞相关的鲁棒耗散的状态反馈控制器.最后,通过例子验证了定理的可行性.     

不确定时滞离散非线性系统的鲁棒耗散滤波

研究了一类带参数不确定性和非线性动态的离散时滞系统的鲁棒耗散滤波问题.所给系统中的不确定项是时变未知且范数有界.基于Lyapunov稳定性方法,先对参数已知而带有非线性动态的时滞离散系统,给出渐近稳定判据,然后讨论鲁棒耗散滤波器的存在条件及设计方法.在此基础上进一步考虑参数不确定性情形,将鲁棒耗散滤波器问题转化为参数确定的情况.从而将鲁棒耗散滤波器的设计问题转换为线性矩阵不等式的求解问题.最后给出仿真例子验证所得结果的有效性.     

基于划分时滞区间的一类Cohen-Grossberg神经网络的鲁棒稳定性

研究一类具有时变时滞及参数不确性的Cohen-Grossberg神经网络的鲁棒稳定性问题.应用划分时滞区间的思想构造了一个新的Lyapunov泛函,并以线性矩阵不等式的形式给出了平衡点全局鲁棒稳定性判据,新判据放松了时变时滞变化率必须小于1的限制.仿真结果进一步证明了所得结论的有效性.     

一类带有时滞的不确定广义系统的切换渐近稳定性

研究了一类带有时滞的切换不确定广义系统的鲁棒渐近稳定问题. 利用Lyapunov稳定性定理和线性矩阵不等式(Linear matrix inequality, LMI)工具, 采用多Lyapunov函数技术, 在设定的切换律下, 得到切换不确定广义时滞系统鲁棒渐近稳定的时滞相关充分条件. 进一步, 建立了一个具有线性矩阵不等式约束的凸优化问题, 利用Matlab软件中的LMI工具箱求解, 得到保证切换广义系统鲁棒渐近稳定的最大可允许时滞上界. 最后示例表明了该方法的有效性.     

含区间时变时滞的线性不确定系统非脆弱鲁棒控制

针对一类时滞是时变的且属于一个已知区间的线性系统,利用Lyapunov-Krasovskii泛函方法,结合积分不等式方法,以线性矩阵不等式的形式,给出了区间时滞线性系统的时滞相关鲁棒稳定性准则,并设计了非脆弱鲁棒控制器。数值算例表明,所得结论是有效的,具有更低的保守性。     

具有时滞的线性区间系统的鲁棒稳定性

本文给出了线性区间时滞系统鲁棒稳定性的一些结果，这些结果推广和改进了前人关于线性时滞系统鲁棒稳定性的相关结论，同时还讨论了线性区间时滞系统的稳定度，最后讨论了线性区间时滞大系统的鲁棒稳定性．     

时滞线性区间系统的鲁棒稳定与鲁棒镇定

利用一个微分不等式给出了几类具有区间 系数的时滞系统的鲁棒稳定和鲁棒镇定的充分条件,这些条件只需判断一个常数矩阵是否为 M矩阵,使用方便．     

区间时滞相关离散非线性系统的鲁棒模型预测控制

针对一类带有扰动、输入约束和凸多面体不确定性的区间时滞离散非线性系统, 提出一种鲁棒模型预测控制方法. 一方面, 利用min-max 模型预测控制求解鲁棒模型预测控制器, 以研究鲁棒预测控制在范数有界意义下的扰动抑制问题; 另一方面, 充分利用时滞的上下界信息构造Lyapunov 函数以得到控制器存在的充分条件. 最后给出了闭环系统鲁棒稳定性证明.     

基于MATLAB不确定线性时滞切换系统的鲁棒性能分析

研究了一类不确定线性时滞切换系统的鲁棒性能。系统不仅状态矩阵带有参数不确定性，而且状态时滞矩阵也带有参数不确定性。根据李亚普诺夫稳定性理论，利用线性矩阵不等式和凸组合条件，给出了该切换系统渐近稳定的充分条件和性能指标，并给出了切换律。最后使用MATLAB的仿真结果表明此方法的正确有效性。     

具有时滞的线性区间系统的鲁棒稳定性

本文给出了线性区间时滞系统鲁棒稳定性的一些结果，这些结果推广和是了前人关于线性时滞系统鲁棒稳定性的相关结论，同时还讨论了线性区间时滞系统的稳定度，最后讨论了线性区间时滞大系统的鲁棒稳定性。     

Robust stability criteria for dynamical systems including delayedperturbations

Considers the problem of robust stability of uncertain time-delay dynamical systems. A new robust stability criteria for linear dynamical systems subject to delayed time-varying and nonlinear perturbations is derived. The results obtained in this note are less conservative than the ones reported so far in the literature. Some analytical methods are employed to investigate the bound on the perturbations so that the systems are stable. A numerical example is given to demonstrate the utilization of the authors' results     

Robust stability of a class of uncertain nonlinear dynamical systems with time-varying delay

We consider the problem of robust stability of a class of uncertain nonlinear dynamical systems with time-varying delay. Based on the assumption that the nominal system (i.e. the system in the absence of uncertainty and delay) is stable, we derive some sufficient conditions on robust stability of uncertain nonlinear dynamical systems with time-varying delay. Some analytical methods and the Bellman-Gronwall inequality are used to investigate such sufficient conditions. The notable features of the results obtained in this paper are their simplicity in testing the stability of uncertain dynamical systems with delay and their clarity in giving an insight into system analysis. Our results are also applicable to perturbed time-delay dynamical systems without exact knowledge of the delay. In addition, a numerical example is given to demonstrate the validity of our results.     

Stability of continuous and discrete time-delay grey systems

In this paper, we have investigated the stability and decaying rate testing problems of grey systems with time delay. Both continuous and discrete time-delay grey systems are discussed whose state matrices are interval matrices. In terms of the Gersgorin theorem, several new delay-independent criteria have been developed to preserve the system stability. By these conditions, new delay-dependent criteria are also presented in order to guarantee that the above-mentioned systems are stable with a specified decay rate. As far as we are aware, this paper seems to be the first to discuss robust stability problems for continuous and discrete time-delay grey systems. Finally, the applications of the results obtained have been illustrated by given numerical examples. We believe that the proposed schemes are applicable to robust control design.     

时滞大系统的Robust稳定性

在本文中考虑了由非线性扰动子系统组成的时滞大系统的鲁棒稳定性问题，利用Ｌｙａｐｕｎｏｖ稳定性准则，对角占优矩阵的方法和结合矩阵Ｒｉｃｃａｔｉ方程，获得了系统指数稳定的充分判据，本文的结果改进并推广了文（４，６）的结果。     

New Robust Stability Conditions and Design of Robust Stabilizing Controllers for Takagi–Sugeno Fuzzy Time-Delay Systems

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.     

Lurie滞后反馈控制系统绝对稳定的鲁棒扰动界

本文应用Lyapunov方法讨论了具有时滞反馈的 Lurie控制系统的鲁棒绝对稳定性,给出了具有一个和多个滞后反馈的Lurie控制系统的绝对 鲁棒稳定的充分条件．用本文的结论可直接计算具有时滞反馈的Lurie控制系统绝对稳定的 鲁棒扰动上界．文末给出了应用本文结论的例子．     

时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.