具有任意未知常时滞系统的鲁棒稳定性(英)

本文采用李雅普诺夫泛函法和一个矢量不等式建立了若干具有任意未知常时滞系统的鲁棒稳定性判据．所获得结果是时滞无关的、文中示例说明了所得稳定性判据减少了现存结果的保守性．     

非线性广义系统时滞相关的模糊控制

研究T-S模糊广义时滞系统的时滞相关稳定性问题．通过定义新的Lyapunov函数,给出时滞相关稳定性判据．进一步考虑模糊权重的作用,将不同子系统间的相互影响考虑到一个矩阵中,给出放宽的模糊控制器设计方案．数值算例表明所得结论较已有文献具有较小的保守性．     

时变时滞离散广义Markov 跳变系统的鲁棒稳定性

研究一类具有区间时变时滞的离散不确定广义Markov跳变系统的时滞相关鲁棒稳定性问题.通过将Jensen不等式与一个新的定界不等式相结合,得到了一个新的稳定性判据,该判据中仅含有Lyapunov变量,具有较小的计算负担.进而,基于凸组合方法得到了另一个新的稳定性判据,该判据引入了一些自由矩阵变量,具有较小的保守性.数值算例表明了所提出方法的有效性.     

具有多个时变时滞的不确定系统的时滞相关稳定性

研究了具有多个时变时滞的不确定系统的 稳定性问题, 利用Razumikhn定理与向量不等式的方法, 给出了不确定时滞系统稳定的充分 条件. 所得的条件与时滞相关, 在很大程度上降低了现有结果的保守性. 文末给出了一个应 用的算例, 并与已有的结果作了比较.     

时滞项可微系统的时滞依赖的稳定性条件

本文研究了带有可微时滞项连续系统的稳定性问题. 通过利用时滞项导数的信息, 给出了改进的时滞系统渐近稳定性条件. 与已有的做法不同, 即便是时滞项导数的上界大于等于 1 时这个上界仍可被利用. 文中证明了所得结果比已有结果的保守性小. 同时, 由于涉及较少的决策变量, 计算复杂度也大为降低. 数例进一步说明了所得结果的有效性和少保守性.     

基于二次分离方法的时变时滞系统稳定性分析

基于二次分离方法研究时变时滞系统的时滞相关稳定性问题.通过引入更为严格的积分二次约束,取得保守性更小的稳定性判据.借鉴时变时滞分解思想,提出基于线性矩阵不等式的改进的稳定性判据.数值算例表明了所提出方法的有效性.     

一类区间时变时滞系统的稳定性分析

针对一类区间时变时滞系统的稳定性问题,进行了全局渐近稳定性分析.通过引入时滞分段方法和构建恰当的Lyapunov-Krasovskii泛函,得到了新的区间时滞相关稳定性判定准则.该准则以线性矩阵不等式形式给出,便于利用LMI工具箱对系统的稳定性进行判定.新准则具有较少的保守性,并且在一定范围内保守性随着时滞分段增多而减少,即时滞分段越多,保守性越少.数值仿真算结果例表明了新准则所具有的有效性和较少的保守性.     

具有多个时滞的积分时滞系统的稳定性分析

首先,针对具有多个时滞的积分时滞系统,建立新的基于线性矩阵不等式的稳定性条件.该条件与正整数k有关,给出$k=1$时该条件与现有结果间的关系.该关系表明所提出条件在$k\geqslant2$时的保守性比现有结果小;然后,基于所提出的稳定性条件,进一步研究具有参数不确定性的积分时滞系统的鲁棒稳定性问题,建立基于线性矩阵不等式的充分条件;最后,利用所提出方法,研究具有多个离散时滞和分布时滞的积分时滞系统的稳定性问题.数值算例结果表明了所提出稳定性判据的有效性.     

时滞系统时滞相关型稳定性准则

针对常数时滞线性系统的稳定性问题,基于一个适当形式的Lyapunov-Krasovskii泛函,通过利用一个积分不等式,采用时滞分解方法,以线性矩阵不等式的形式给出了时滞系统的时滞相关型稳定性准则.与现有的时滞相关型稳定性结果相比较,所得到的结果具有保守性更好,结构更加简单,且不合有任何多余的矩阵变量等特点,并从理论上进行了严格的证明,解决了现有的稳定性结果绝大多数只是从数值例子说明其有效性的问题.示例说明了所得结果的有效性.     

具有任意未知常时滞系统的鲁棒稳定性

本文采用李雅普诺夫泛函法和一个矢量不式建立了若干具有任意未知常时滞系统的鲁棒稳定性判据，所获得结果是时无关的，文中示例说明了所得稳定性判据减少了现存结果的保守性。     

Stability analysis and stabilization of Markovian jump systems with time‐varying delay and uncertain transition information

The paper investigates the problems of stability and stabilization of Markovian jump systems with time‐varying delays and uncertain transition rates matrix. First, the stochastic scaled small‐gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov‐Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method.     

New stability criterion for linear switched systems with time‐varying delay

This paper studies the stability problem of a class of linear switched systems with time‐varying delay in the sense of Hurwitz convex combination. By designing a parameter‐dependent switching law and using a new convex combination technique to deal with delay terms, a new stability criterion is established in terms of LMIs, which is dependent on the parameters of Hurwitz convex combination. The advantage of the new criterion lies in its less conservatism and simplicity. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

短时滞的网络控制系统稳定性分析

针对具有时变传输时滞和间隔的网络控制系统(Networked Control Systems,NCSs)进行分析,基于传输时滞及输入时滞构建一种新的依赖于时间的非连续的Lyapunov泛函,提出新的稳定性准则。考虑零阶保持器更新时间在两个有效采样时间范围内,结合缩放方法及凸优化技术,最后通过线性矩阵不等式计算,得到新的稳定性准则能减少系统保守性。与其它方法相比,本文提出的方法具有更小的保守性。     

New delay-dependent exponential stability for neural networks with time delay.

In this correspondence, the problem of exponential stability for neural networks with time delay is investigated. By introducing a novel Lyapunov-Krasovskii functional with the idea of delay fractioning, a new criterion of exponential stability is derived and then formulated in terms of a linear matrix inequality. This new criterion proves to be much less conservative than the most recent result, and the conservatism can be notably reduced as the fractioning goes thinner. An example is provided to demonstrate the advantage of the proposed result.     

New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay

This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By using the discrete Jensen inequality and the sector bound conditions, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.     

MIMO网络控制系统的稳定性与控制器设计

对于具有多个独立传感器与执行器的多输入多输出网络控制系统,在具有多重时滞的情况下,建立一类网络控制系统的连续时间模型。通过构造一个新的李雅普诺夫函数,给出一个具有较低保守性的稳定性判据。基于该稳定性判据,给出输出反馈控制器的设计方法,数值仿真结果表明了该方法的有效性。