Stability analysis of uncertain neutral systems with discrete and distributed delays via the delay partition approach

This paper focuses on the stability analysis for neutral systems with discrete and distributed constant time-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delay interval into multiple segments and choosing proper functionals with different weighting matrices coressponding to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the neutral system in the delay partition approach. By utilizing the delay partition approach, the obtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.     

A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay

This paper is concerned with delay-dependent passivity analysis for interval neural networks with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these new LKFs, a new passivity criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of the time delay. Finally, some numerical examples are given to illustrate the effectiveness of the developed techniques.     

Global Passivity Analysis of Interval Neural Networks with Discrete and Distributed Delays of Neutral Type

This paper is concerned with delay-dependent passivity analysis for delayed neural networks (DNNs) of neutral type. We first discuss the passivity conditions for DNNs without uncertainties and then extend this result to the case of interval uncertainties. By partitioning the delay intervals into multiple equidistant subintervals, some appropriate Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Considering these new LKFs and using free-weighting matrix approach, several new passivity criteria are proposed in terms of linear matrix inequalities, which are dependent on the size of the time delay. Finally, five numerical examples are given to illustrate the effectiveness and less conservatism of the developed techniques.     

New conditions for delay-derivative-dependent stability

Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov–Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.     

Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

This paper presents new exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub‐interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed‐state‐feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed‐state‐feedback stabilization problem for a nonlinear uncertain stochastic time‐delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.     

WDOP‐based Summation Inequality and its Application to Exponential Stability of Linear Delay Difference Systems

This paper is concerned with the exponential stability analysis of linear delay difference systems. Firstly, a set of weighted discrete orthogonal polynomials (WDOPs) is established by using the Gram‐Schmidt orthogonalization process, and then two WDOPs‐based summation inequalities, including some existing summation inequalities as special cases, are developed. Secondly, these WDOPs‐based summation inequalities are applied to investigate the exponential stability criteria and explicit exponential estimates of solutions of linear delay difference systems. Finally, two numerical examples indicate that the proposed WDOPs‐based approach can derive the exponential stability condition with larger decay rate than the existing ones.     

单滞后时变区间动力系统的指数稳定性

用矩阵测度和时滞微分不等式研究了单滞后时变区间动力系统 x(t) =N[P(t) ,Q(t) ]x(t) +N[C(t) ,D(t) ]x(t -τ) ,τ≥ 0 的指数稳定性 ,给出了其指数稳定的判别准则 ,推广和改进了文 [1～ 3]的工作     

New results on stability analysis of singular time-delay systems

This paper deals with the problem of delay-dependent stability analysis for singular systems with a constant time delay. By employing the Jensen inequality and the Wirtinger-based inequality, new delay-dependent stability criteria are developed. Furthermore, in order to obtain less conservative results, a new method of constructing Lyapunov--Krasovskii functionals (LKFs) is used. It should be pointed out that the positive-definiteness restrictions on some symmetric matrices of the LKFs are removed. All the criteria are proposed in terms of strict linear matrix inequalities. Finally, numerical examples are given to demonstrate the less conservatism of the results.     

非线性随机时滞系统的稳定性与应用

首先考虑了不确定性的一族非线笥随机时滞系统,建立了这种系统的均方指数稳定与几乎必须指数稳定的充分准则,其准则是时滞无关的,然后应用这些充分条件到一类不确定的随机时滞神经网络,得到了这咱神经网络指数稳定的产用判据。本文的结果是最近文献中某些结果的推广,最后一个数值例子说明的所给准则的有效性。     

Delay-Dependent Exponential Stability of Neutral Stochastic Delay Systems

This technical note studies stability of neutral stochastic delay systems by linear matrix inequality approach. Delay-dependent criterion for exponential stability is presented and numerical examples are conducted to verify the effectiveness of the proposed method.     

具有时变不确定性的脉冲时滞大系统的鲁棒稳定性

提出并研究了具有时变不确定性的脉冲时滞大系统的鲁棒稳定性,借助于向量比较原理和矩阵不等式等方法,对该系统建立了若干大范围指数鲁棒稳定的判据,并举例说明了结论的有效性。     

Robust Exponential Stability of Discrete‐Time Delay Impulsive Systems with Parametric Uncertainties

This paper investigates robust exponential stability for discrete‐time delay impulsive systems with parametric uncertainties. The parametric uncertainties in the systems are assumed to be time varying and norm bounded. Using Lyapunov functionals, some robust exponential stability criteria are given. It is shown that the time interval between the nearest two impulses should be small enough, i.e., impulses must act frequently, when the impulses are employed to stabilize the original impulse‐free system that is not robustly stable. Conversely, when the original system without impulses is robustly stable, the time interval between the nearest two impulses should be large enough to let the system with impulsive perturbations retain its stability property. It should be noted that this is the first time that impulsive robust exponential stabilization results are given via Lyapunov functionals for discrete‐time uncertain delay impulsive systems. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.     

具有区间时滞的不确定性随机时滞系统的时滞相关鲁棒稳定性

针对具有区间时滞的不确定性随机时滞系统, 进行稳定性分析. 通过考虑变时滞、时滞的上界及它们的差三者之间的关系, 并应用公式和Lyapunov稳定性理论, 在不忽略任何有用项的前提下, 得到改进的具有区间时滞的随机系统的稳定性判据. 数值实例验证了该方法的有效性.     

Exponential Stability and Stabilization for Quadratic Discrete‐Time Systems with Time Delay

In this note, we deal with the exponential stability and stabilization problems for quadratic discrete‐time systems with time delay. By using the quadratic Lyapunov function and a so called ‘Finsler's lemma', delay‐independent sufficient conditions for local stability and stabilization for quadratic discrete‐time systems with time delay are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.     

区间变时滞不确定线性系统带记忆H∞状态反馈控制

一类存在范数有界不确定性的线性时变时滞系统, 其时变时滞仅给出时滞变化的上下界, 而对时滞变化率未作任何约束. 对于这类区间时变时滞系统, 给出了一种新型的 Lyapunov-Krasovskii 泛函讨论其稳定性, 通过分割平均时滞的方法减小保守性, 得到以线性矩阵不等式(LMI)形式给出的稳定性判据. 最后分析并给出了一种带记忆的 H∞ 状态反馈控制器. 数值实例表明了本文方法的有效性.     

New stability criteria for BAM neural networks with time-varying delays

In this paper, the exponential stability is investigated for a class of time-delay BAM neural networks (NNs). Time delays of two layers are taken into account separately rather than as a whole with the idea of delay fractioning. Then we generalize the result to time-varying interval delay condition. Exploiting the known constant part of delay sufficiently to estimate the upper bounds, we can derive an improved stability for BAM NNs with time-varying interval delay. Two examples are provided to demonstrate the less conservatism and effectiveness of the proposed linear matrix inequality (LMI) conditions.     

Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses

In this paper, the problem of neutral-type impulsive bidirectional associative memory neural networks (NIBAMNNs) with time delays are first established by a Takagi-Sugeno (T-S) fuzzy model in which the consequent parts are composed of a set of NIBAMNNs with interval delays and Markovian jumping parameters (MJPs). Sufficient conditions to check the robust exponential stability of the derived model are based on the Lyapunov-Krasovskii functionals (LKFs) containing some novel triple integral terms, Lyapunov stability theory and employing the free-weighting matrix method. The delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs), which can be very efficiently solved using Matlab LMI control toolbox. Finally, numerical examples and remarks are given to illustrate the effectiveness and usefulness of the derived results.     

时滞切换系统指数稳定性分析: 多Lyapunov函数方法

将多 Lyapunov 函数方法推广至时滞情形, 分析切换与时滞对于稳定性的影响. 以 Halanay 不等式为引理, 给出了与时滞相关的切换序列约束条件, 以保证系统的指数稳定性. 若时滞项消失, 本文关于切换对于稳定性影响的分析与无时滞情形的相关结论是一致的. 仿真结果说明了本文方法的有效性.     

Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay

In this paper, we are concerned with the problem of stability analysis and stabilization control design for Takagi–Sugeno (T–S) fuzzy systems with probabilistic interval delay. By employing the information of probability distribution of the time delay, the original system is transformed into a T–S fuzzy model with stochastic parameter matrices. Based on the new type of T–S fuzzy model, the delay-distribution-dependent criteria for the mean-square exponential stability of the considered systems are derived by using the Lyapunov–Krasovskii functional method, parallel distributed compensation approach, and the convexity of some matrix equations. The solvability of the derived criteria depends not only on the size of the delay but also on the probability distribution of the delay taking values in some intervals. The revisions of the main criteria in this paper can also be used to deal with the case when only the information of variation range of the delay is considered. It is shown by practical examples that our method can lead to very less conservative results than those by other existing methods.      

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...