A new admissibility condition of discrete-time singular systems with time-varying delays

This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.     

Delay dependent robust stability of singular systems with additive time-varying delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.     

时滞切换系统的时滞依赖稳定

首先利用多Lyapunov 函数方法, 分析常时滞切换系统的时滞依赖稳定性, 并给出此系统时滞依赖稳定的充分条件及切换律的设计; 然后运用共同Lyapunov 函数方法, 研究一类时变时滞切换系统的时滞依赖稳定性, 也给出此系统时滞依赖稳定的充分条件及切换律的设计. 所得结果均可用线性矩阵不等式方法求解. 最后通过仿真验证了结论的正确有效性.     

模型相关时变时滞马尔可夫跳变系统低保守稳定性

本文研究了时变时滞与模型相关的随机马尔可夫跳变系统的时滞相关稳定性问题. 通过建立时变时滞与模型相关的系统模型, 构造不同的Lyapunov-Krasovskii函数, 并通过引入改进的积分等式, 以线性矩阵不等式的形式提出了具有较小保守性的时滞依赖稳定性条件. 最后用几个数值算例说明本文结论的有效性及较低的保守性.     

离散奇异时滞系统时滞依赖稳定性分析与镇定

分别研究了离散奇异时滞系统时滞依赖稳定性分析与镇定问题. 首先给出了一个新的离散奇异时滞系统时滞依赖容许性充分条件. 经过证明, 所提出的方法与现有结论相比, 具有一定的优势. 然后, 运用矩阵理论技巧,设计出状态反馈控制器保证闭环离散奇异时滞系统是容许的. 最后,两个数值例子说明了所用方法的有效性.     

Delay-dependent Non-fragile H∞ Filtering for Uncertain Fuzzy Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function

This paper is concerned with the non-fragile H∞ filter design problem for uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay. To begin with, the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Then, based on the piecewise Lyapunov function and matrix decoupling technique, a new delay-dependent non-fragile H∞ filtering method is proposed for the switching fuzzy system. The proposed condition is less conservative than the previous results. Since only a set of LMIs is involved, the filter parameters can be solved directly. Finally, a design example is provided to illustrate the validity of the proposed method.     

非相称多时滞奇异系统的有记忆状态反馈控制

针对一类非相称多时滞奇异系统, 研究其时滞相关稳定性问题. 给出了易于数值检验的时滞无关正则条件. 基于Lyapunov-Krasovskii泛函方法和广义积分引理给出了系统时滞相关稳定的充分条件. 本文的主要思想是利用矩阵不等式方法, 设计有记忆状态反馈控制器, 使相应的闭环系统时滞无关正则、无脉冲、渐进稳定, 并直接给出了有记忆状态反馈控制器参数化的表达形式. 最后通过数值仿真验证了所提方法的有效性.     

不确定广义时滞依赖鲁棒H∞控制

This paper discusses the problem of delay-dependent robust Ha control for uncertain singular systems with state delay. Based on linear matrix inequality (LMI) approach, we design a state feedback controller, which guarantees that, for all admissible uncertainties, the resultant closed-loop system is regular, impulse free, and stable with an H<,∞> norm bound constraint. All the obtained results are delay-dependent and formulated by strict LMI involving no decomposition of the system matrices. Numerical examples show that the proposed methods are less conservative than existing ones.     

针对准单边Lipschitz不确定非线性时滞系统的稳定性分析

研究了一类不确定非线性时滞系统的鲁棒稳定性. 准单边Lipschitz条件被介绍, 并被用于估计非线性向量函数在稳定性分析中的影响. 线性矩阵不等式形式的时滞无关/时滞相关稳定性判据被得到. 此外, 即使系统系数是不稳定的, 这些稳定性判据也是可利用的, 因为未必正定的准单边Lipschitz常数矩阵包含了很多非线性部分的有用信息. 数值实例证实了本文所获结果的有效性.     

广义时滞系统的时滞依赖L2-L∞滤波

讨论广义时滞系统的L2-L∞滤波问题. 目的是设计全阶滤波器保证滤波误差系统的时滞依赖指数允许性和给定的L2-L∞性能指标. 通过解线性矩阵不等式获得所需的滤波器. 数值例子表明结果具有较小的保守性.