Stability Analysis of Takagi–Sugeno Fuzzy Cellular Neural Networks With Time-Varying Delays

This correspondence investigates the global exponential stability problem of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays (TSFDCNNs). Based on the Lyapunov-Krasovskii functional theory and linear matrix inequality technique, a less conservative delay-dependent stability criterion is derived to guarantee the exponential stability of TSFDCNNs. By constructing a Lyapunov-Krasovskii functional, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is released in the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the effectiveness of the proposed results     

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.     

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.     

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.     

Exponential stability analysis for neutral BAM neural networks with time-varying delays and stochastic disturbances

This paper is concerned with the global exponential stability analysis problem for a class of neutral bidirectional associative memory (BAM) neural networks with time-varying delays and stochastic dist...     

New delay-dependent global asymptotic stability condition for Hopfield neural networks with time-varying delays

This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.     

区间时变细胞神经网络的全局鲁棒指数稳定性

研究了一类区间时变扰动、变时滞细胞神经网络的全局鲁棒指数稳定性问题．利用Leibniz-Newton公式对原系统进行模型变换,并分析了变换模型和原始模型的等价性．基于变换模型,运用线性矩阵不等式的方法,通过选择适当的Lyapunov-Krasovskii泛函,推导了该系统全局鲁棒指数稳定的时滞相关的充分条件．通过数值实例将所得结果与前人的结果相比较,表明了本文所提出的稳定判据具有更低的保守性．     

Delay Dependent Exponential Stability for Fuzzy Recurrent Neural Networks with Interval Time-Varying Delay

In this paper, the problem of delay-dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay is investigated. The delay interval has been decomposed into multiple non equidistant subintervals, on these interval Lyapunov-Krasovskii functionals (LKFs) are constructed to study stability analysis. Employing these LKFs, an exponential stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs) which can be easily solved by MATLAB LMI toolbox. Numerical example is given to illustrate the effectiveness of the proposed method.     

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

     

经过一种PTVD补偿的带有快变中立型时滞的系统的时滞依赖稳定性

研究了一类带有时变时滞的线性中立型系统的稳定性, 其中中立型项中的时滞包括一类快变时滞(即, 时滞导数大于1). 目前, 还没有文献考虑带有这种带有快变中立型时滞的系统. 通过使用新的Lyapunov-Krasovskii泛函和带有时滞的多项式(PTVD)补偿技术, 对于此类系统提出了具有更少保守性的时滞依赖稳定性判据. 通过使用新的泛函可以实现处理快变时滞的目的. 同时, 通过使用PTVD补偿技术, 可以在判据中引入一些有用的元素. 而在之前的结果中, 当估计Lyapunov-Krasovskii泛函的上界时, 这些元素通常是被忽略的. 一个数值例子将被提供来验证所得到结果的有效性.     

Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays

This paper is concerned with the robust delay-dependent exponential stability of uncertain stochastic neural networks (SNNs) with mixed delays. Based on a novel Lyapunov-Krasovskii functional method, some new delay-dependent stability conditions are presented in terms of linear matrix inequalities, which guarantee the uncertain stochastic neural networks with mixed delays to be robustly exponentially stable. Numerical examples are given to illustrate the effectiveness of our results.     

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.     

New stability analysis for generalized neural networks with interval time-varying delays

This paper deals with the problem of delay-dependent stability for neural networks with interval time-varying delays. First, we divided delay interval into two parts. Second, a new Lyapunov-Krasovskii functional is constructed, and relationships between the augmented state vectors have been fully considered, which may yield less conservative results. Third, based on free-matrix-based integral inequality method and reciprocally convex technique, some new less conservative delay-dependent stability criteria have been obtained by combining with the new Lyapunov-Krasovskii functional. Finally, two numerical examples are given to show the effectiveness of the derived conditions over the existing ones.     

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。     

具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据

研究一类具有非线性扰动的时变时滞中立型系统鲁棒稳定性问题。基于直接Lyapunov Krasovskii泛函并结合自由权矩阵方法的分析方法,建立了线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关稳定性判据。与以往方法不同,在处理泛函导数时,该方法不包含任何模型变换和涉及交叉项的处理,只是通过引入相关项自由权矩阵,充分考虑各项之间的相互关系,降低了结论的保守性。最后,利用Matlab的LMI工具箱进行了的数值仿真, 算例仿真表明所提出的判据的有效性。     

Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks

This paper is devoted to investigating delay-dependent robust exponential stability for a class of Markovian jump impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks (IRDCGNNs) with mixed time delays and uncertainties. The jumping parameters, determined by a continuous-time, discrete-state Markov chain, are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing a Lyapunov–Krasovskii functional, and using poincarè inequality and the mathematical induction method, several novel sufficient criteria ensuring the delay-dependent exponential stability of IRDCGNNs with Markovian jumping parameters are established. Our results include reaction-diffusion effects. Finally, a Numerical example is provided to show the efficiency of the proposed results.     

混合变时滞不确定中立型系统鲁棒稳定性分析

研究一类含混合变时滞不确定中立系统时滞相关鲁棒稳定性问题。基于时滞中点值,把时滞区间均分成两部分,通过构造包含时滞中点信息的增广泛函和三重积分项的Lyapunov-Krasovskii (L-K)泛函,利用L-K稳定性定理、积分不等式方法和自由权矩阵技术,建立了一种基于线性矩阵不等式(LMI)的、与离散时滞和中立时滞均相关的鲁棒稳定性判据。数值算例表明,该判据改善了已有文献的结论,具有更低的保守性。     

Passivity-based decentralized stabilization of multi-agent systems with uncertainty and mixed delays

In this paper, we investigate a decentralized stabilization problem of uncertain multi-agent systems with mixed delays including discrete and distributed time-varying delays based on passivity stability. We design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent passivity stability for each subsystem. Then, by employing a new Lyapunov-Krasovskii function, a linear matrix inequality （LMI） approach is developed to establish the delay-dependent criteria for the passivity stability of multi-agent systems. The sufficient condition is given for checking the passivity stability. The proposed LMI result is computationally efficient. An example is given to show the effectiveness of the method.