Delay-range-dependent stability criterion for interval time-delay systems with nonlinear perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality (LMI) framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.     

奇异时滞系统的时滞依赖稳定性判据

讨论了奇异时滞系统的稳定性问题. 首先, 在几个最新的结果之间建立了等价性, 并给出了一个简化的稳定性判据. 然后, 通过使用时滞分解的方法, 得到了一个新的稳定性判据. 它比现有结果具有更少的保守性. 最后, 给出了一个数值例子, 表明了新判据是有效的且保守性较小.     

New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks

The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov–Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results.     

具有区间时滞的离散时间基因调控网络稳定性研究

针对具有随机干扰和区间时滞的离散时间基因调控网络(GRNs),基于Lyapunov稳定性定理,利用改进型自由权矩阵方法研究其时滞相关稳定问题.通过考虑时变时滞、时滞上界及它们的差三者之间的关系,同时保留增广Lyapunov-Krasovskii泛函差分中的所有有用项,获得一种更低保守性的时滞相关渐近稳定新判据.最后,给出仿真实例验证本文方法的有效性及相比已有方法的优越性.     

Design of sampled-data control for multiple-time delayed generalised neural networks based on delay-partitioning approach

In this paper, we addressed the problem of stability analysis for a class of generalised mixed delayed neural networks by delay-partitioning approach. A novel integral inequality is developed by employing Wirtinger's integral inequality and Leibniz–Newton formula. By constructing an augmented Lyapunov–Krasovskii functional with triple and quadruple integral terms and using some standard integral inequality techniques, asymptotic stability criterion is obtained to the concerned neural networks. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered generalised neural networks are derived in terms of a dynamic system with sampling. Finally, numerical examples are given to show that the proposed method is less conservative than existing ones.     

New Delay-Dependent Stability Results for Neural Networks With Time-Varying Delay

This paper studies the problem of stability analysis for neural networks (NNs) with a time-varying delay. Unlike the previous works, the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By defining a more general type of Lyapunov functionals, some new less conservative delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs). Meanwhile, the computational complexity of the newly obtained stability conditions is reduced because less variables are involved. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.     

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.     

网络化神经网络的时滞依赖稳定性判据

本文研究了网络化神经网络的稳定性问题.首先,为了利用网络系统的采样特征,定义了一个新的Lyapunov泛函;通过分析网络诱导时延和执行周期之间的关系,采用一个迭代凸组合技术,得到了一个包含较少保守性的稳定性判据.然后,给出一个基于采样数据的神经网络稳定性判据,减少了计算复杂性.最后,通过一个数例,验证了本文方法的有效性和优越性.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

On Improved Delay-dependent Robust Stability Criteria for Uncertain Systems with Interval Time-varying Delay

 This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.     

时滞基因调控网络的全局渐进稳定性分析

针对一类时滞基因调控网络的全局渐进稳定性进行了研究, 利用Lyapunov泛函、线性矩阵不等式（LMIs）和自由权值矩阵（free-weighting matrices）技术, 得到了一些新的时滞相关的基因调控网络稳定性充分条件。通过在Lyapunov泛函中使用辅助矩阵E, 并对调控函数条件一般化, 取得的结果具有较少的保守型和更广的适用性。该结果为人工设计基因芯片提供一定的参考作用。仿真示例进一步验证了结论的有效性。     

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.     

线性时滞系统的时滞相关鲁棒稳定性新判据

讨论具有多个范数有界不确定的线性时滞系统的时滞相关鲁棒稳定性.利用Lyapunov-Krasovskii泛函方法,结合自由权矩阵思想,在Lyapunov-Krasovskii泛函的导数中恰当地引入一些自由矩阵,获得了基于线性矩阵不,等式的时滞相关稳定充分条件.该条件较已有结论不仅形式简单,而且具有更小的保守性.     

H∞ control for discrete‐time Markovian jump systems with partial information on transition probabilities

This paper focuses on mode‐dependent H_∞ state‐feedback control for a class of discrete‐time Markovian jump systems (MJSs) with partial information on transition probabilities (TPs). The augmented free‐connection weighting matrices are introduced by considering the influence of partial information of TPs on discrete‐time MJSs and the disturbance input on the state vector. As a result, the less conservative stability criterion and bounded real lemma (BRL) of MJSs with partly unknown TPs are obtained. Then the sufficient conditions for designing the mode‐dependent H_∞ controllers are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness and the merits of the proposed method.     

A less conservative robust stability criteria for uncertain neutral systems with mixed delays

This paper is concerned with the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. By considering the cross-terms with additional design parameters, a complete form of Lyapunov–Krasovskii functional is constructed. Then some free weighting matrices are introduced, and a sufficient stability condition is obtained in terms of linear matrix inequalities. The obtained criterion is dependent on the sizes of neutral delay and discrete delay and are less conservative than those produced by previous approaches. Numerical examples are given to illustrate both the improvement the proposed method provides over some existing ones and the relationship between the neutral- and discrete-delay.     

A delay-dependent passivity criterion of linear neutral delay systems

The problem of delay-dependent stability and passivity for linear neutral systems is discussed. By constructing a novel type Lyapunov-krasovskii functional, a new delay-dependent passivity criterion is presented in terms of linear matrix inequalities （LMIs）. Model transformation, bounding for cross terms and selecting free weighting matrices [12-14] are not required in the arguments. Numerical examples show that the proposed criteria are available and less conservative than existing results .     

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.     

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.     

不确定线性多时变时滞系统的时滞相关鲁棒控制

提出一种积分不等式新方法，讨论不确定线性多时变时滞系统的鲁棒稳定性以及鲁棒稳定化问题，首先利用Park不等式建立了基于二次型项的积分不等式，利用这一不等式获得了系统基于LMI的时滞相关、时滞导数相关鲁棒稳定条件；然后利用这一条件给出了时滞状态反馈控制器的一种新的设计方法，数值例子说明了所得结论具有较小的保守性。     

Stability analysis of Takagi-Sugeno stochastic fuzzy Hopfield neural networks with discrete and distributed time varying delays

In this paper, the global stability problem of Takagi-Sugeno (T-S) stochastic fuzzy Hopfield neural networks (TSSFHNNs) with discrete and distributed time varying delays is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSSFHNNs with discrete and distributed time varying delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain stability region. In fact, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. The proposed stability conditions are demonstrated with numerical examples. Comparison with other stability conditions in the literature shows that our conditions are the more powerful ones to guarantee the widest stability region.