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.     

On the stability of uncertain systems with multiple time-varyingdelays

In this paper, criteria for the global asymptotic stability of a class of uncertain systems with multiple time-varying delays are proposed. Based on the improved Razumikhin-type theorem, delay-dependent and delay-independent criteria are provided to guarantee the global asymptotic stability of such systems. Our main results are generalizations of some recent results reported in the literature in the case with multiple time-varying delays. A numerical example Is also given to illustrate our results     

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.     

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     

Robust stability for uncertain neutral systems with mixed time-varying delays

The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality （LMI）. Finally, a numerical example is given to illustrate significant improvement over some existing results.     

On delayed uncertain genetic regulatory networks: robust stability analysis

In this paper, the problem of stability analysis for uncertain genetic regulatory networks with time-varying delays is investigated. The time-varying delay function in this paper is not required to be either continuously differentiable, or its derivative less than one. By choosing an appropriate Lyapunov–Krasovskii functional and employing some free-weighting matrices, some new delay-dependent and delay-derivative-dependent stability criteria are presented in terms of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Finally, three numerical examples are used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.     

New Delay-dependent stability criteria for neutral systems with time-varying delay using delay-decomposition approach

This paper concerns with the problem of asymptotic stability for neutral systems with timevarying delays. With the introduction of delay-decomposition approach, some new delay-dependent stability criteria are established and formulated in the form of linear matrix inequalities. Both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

具有区间时变时滞2-D 离散系统的时滞相关稳定与控制

针对具有区间时变时滞2-D离散系统,利用时滞相关方法,研究其稳定性与控制问题.首先选取含有时滞项上、下界的一个新的Lyapunov函数,对其差分时考虑所有项,得到了基于线性矩阵不等式(LMI)的时滞相关稳定性准则;然后给定时变时滞项的下界,再由一个凸优化问题最大化其上界,进而通过状态反馈实现系统的时滞相关控制,且求解LMI可得到增益矩阵;最后,利用数值算例说明了所得结果有效且优于已有成果.     

Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.      

Further improvement of stability criterion and BRL for Markovian jump systems with interval time-varying delay

This paper deals with delay-dependent stochastic stability and bounded real lemma(BRL)for Markovian jump linear systems with interval time-varying delays.By constructing some new Lyapunov functionals and using the Jensen’s integral inequality method,the free weighting matrix method,the convex combination method and the delay decomposition approach integratedly,some less conservative delay-dependent stability criteria and BRL are established. Numerical examples are given to show the effectiveness of the proposed method.     

Delay-dependent robust H-infinity control for discrete-time uncertain systems with time-varying state delays

1 Introduction The analysis and synthesis of dynamic control systems with time delays is a subject of great practical and theo- retical importance, and has received considerable attention for decades (see [1,2] and references therein). Stability cri- teria can be classified roughly into two categories: delay- independent and delay-dependent [3]. Delay-independent criteria contains no information on the delay size, which, as might be expected, is generally conservative, especially when the dela…     

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.     

基于Jensen 不等式的2-D 区间时变时滞系统的稳定与控制

考虑具有区间时变时滞二维(2-D) 离散系统的时滞相关稳定性和控制问题. 选取含有时滞上下界的Lyapunov 函数, 对其差分时考虑到所有项, 结合2-DJensen 不等式, 由线性矩阵不等式给出系统新的时滞相关稳定性准则. 准则中含有更少的待定变量, 降低了数值计算负担, 并且比一些已有结果具有更小的保守性. 基于稳定性准则, 由状态反馈实现了系统的稳定控制. 最后, 通过数值算例表明了所得结果的有效性和优越性.

     

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.     

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.     

Delay-dependent criteria for robust stability of time-varying delay systems

This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

Anti-periodic solutions for HCNNs with time-varying delays in the leakage terms

In this paper, a class of high-order cellular neural networks model is considered with the introduction of time-varying delays in the leakage terms. By using differential inequality techniques, some very verifiable and practical delay-dependent criteria on the existence and global exponential stability of anti-periodic solution for the model are derived. Even for the model without leakage delays, the criteria are shown to be less conservative than many recent publications. Moreover, some examples and remarks are given to demonstrate the feasibility of our method.     

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying interval delays and Markovian jumping parameters by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of Markovian jumping BAM neural networks with time-varying interval delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite-state space. The new type of Markovian jumping matrices P_k and Q_k are introduced in this paper. The parameter uncertainties are assumed to be norm bounded and the delay is 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. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.