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1.
This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional (LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.   相似文献   

2.
This paper concerns the stability problem of singular systems with time-varying delay. First, the singular system with time-varying delay is transformed into the neutral system with time-varying delay. Second, a more proper Lyapunov–Krasovskii functional (LKF) is constructed by adding some integral terms to quadratic forms. Then, to obtain less conservative conditions, the free-matrix-based integral inequality is adopted to estimate the derivative of LKF. As a result, some delay-dependent stability criteria are given in terms of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method.  相似文献   

3.
This paper studies the problem of stability and dissipativity analysis for uncertain Markovian jump systems (UMJSs) with random time-varying delays. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical tools, a new double integral inequality (NDII) is developed. Then, to show the efficiency of the proposed inequality, a suitable Lyapunov-Krasovskii functional (LKF) is constructed with augmented delay-dependent terms. By employing integral inequalities, new delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness and less conservatism of the results.  相似文献   

4.
This paper represents a novel less conservative stability criterion for time-delay systems with nonlinear disturbances. The main purpose is to obtain larger upper bound of the time-varying delay. A suitable Lyapunov- Krasovskii functional (LKF) with triple integral terms is constructed. Then, two new generalized double integral (GDI) inequalities are proposed which encompass Wirtinger-based double inequality as a special case. A simple case of the proposed GDI inequality is utilized to estimate double integral terms in the time derivative of the constructed LKF. Further, an improved delay-dependent stability criterion is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are given to illustrate the improvement of the proposed criteria.  相似文献   

5.
研究了带有非线性扰动的时变时滞系统的稳定性问题.基于时滞分割方法,提出了保守性更小的系统稳定性分析准则.利用一个自由参数将时滞区间分割为2个子区间,进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函,并采用自由矩阵积分不等式界定泛函导数中的交叉项.基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则.数值算例表明该稳定性准则能够得到更大的时滞上界,与已有结果相比具有更小的保守性.  相似文献   

6.
This paper studies mean square exponential stability of linear stochastic neutral‐type time‐delay systems with multiple point delays by using an augmented Lyapunov‐Krasovskii functional (LKF) approach. To build a suitable augmented LKF, a method is proposed to find an augmented state vector whose elements are linearly independent. With the help of the linearly independent augmented state vector, the constructed LKF, and properties of the stochastic integral, sufficient delay‐dependent stability conditions expressed by linear matrix inequalities are established to guarantee the mean square exponential stability of the system. Differently from previous results where the difference operator associated with the system needs to satisfy a condition in terms of matrix norms, in the current paper, the difference operator only needs to satisfy a less restrictive condition in terms of matrix spectral radius. The effectiveness of the proposed approach is illustrated by two numerical examples.  相似文献   

7.
This study is concerned with the problem of non fragile synchronisation of mixed delayed neural networks with randomly occurring controller gain fluctuations. By using a novel mathematical approach and considering the neuron activation functions, improved delay-dependent stability results are formulated in terms of linear matrix inequalities (LMIs). An augmented new Lyapunov-Krasovskii functional (LKF) that contains double and triple integral terms is constructed to ensure the asymptotic stability of the error system which guarantees the master system synchronise with the slave system. Finally, numerical examples are provided to show the effectiveness of the proposed theoretical results.  相似文献   

8.
This paper investigates the delay-dependent stability problem of recurrent neural networks with time-varying delay. A new and less conservative stability criterion is derived through constructing a new augmented Lyapunov-Krasovskii functional (LKF) and employing the linear matrix inequality method. A new augmented LKF that considers more information of the slope of neuron activation functions is developed for further reducing the conservatism of stability results. To deal with the derivative of the LKF, several commonly used techniques, including the integral inequality, reciprocally convex combination, and free-weighting matrix method, are applied. Moreover, it is found that the obtained stability criterion has a lower computational burden than some recent existing ones. Finally, two numerical examples are considered to demonstrate the effectiveness of the presented stability results.  相似文献   

9.
This paper is concerned with the stability analysis of linear discrete time-delay systems. New discrete inequalities for single summation and double summation are presented to estimate summation terms in the forward difference of Lyapunov-Krasovskii functional (LKF), which are more general than some commonly used summation inequalities. Through the construction of an augmented LKF, improved delay-dependent stability criteria for discrete time-delay systems are established. Based on this, a time-delayed controller is derived for linear discrete time-delay systems. Finally, the advantages of the proposed criteria are revealed from the solutions of the numerical examples.  相似文献   

10.
This brief is concerned with asymptotic stability of neural networks with uncertain delays. Two types of uncertain delays are considered: one is constant while the other is time varying. The discretized Lyapunov–Krasovskii functional (LKF) method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks (DNNs). A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing stability criteria.   相似文献   

11.
肖伸平  练红海  陈刚  冯磊 《控制与决策》2017,32(6):1084-1090
研究时变时滞神经网络的鲁棒稳定性和耗散性问题.充分利用积分项的时滞信息和激励函数条件构造一个合适的增广LK泛函;利用自由矩阵积分不等式处理LK泛函的导数,得到一个低保守性的时滞相关稳定判据;将所获得的结论延伸至神经网络的耗散性分析,并推导出一个确保神经网络严格$(\mathcalX, \mathcalY,\mathcalZ)-\gamma$-耗散的充分条件.最后通过3个数值算例验证了所提出方法的可行性和优越性.  相似文献   

12.
This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov–Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained results.  相似文献   

13.
 This paper considers the problem of delay-dependent non-fragile H control for a class of linear systems with interval time-varying delay. Based on the direct Lyapunov method, an appropriate Lyapunov-Krasovskii functional (LKF) with triple-integral terms and augment terms is introduced. Then, by using the integral inequalities and convex combination technique, an improved H performance analysis criterion and non-fragile H controller are formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by using standard numerical packages. At last, two numerical examples are provided to demonstrate the effectiveness of the obtained results.  相似文献   

14.
This paper is concerned with delay-dependent stability analysis and stabilization problems for continuous-time Takagi and Sugeno (T-S) fuzzy systems with a time-varying delay. A new method for the delay-dependent stability analysis and stabilization is suggested, which is less conservative than other existing ones. First, based on a fuzzy Lyapunov-Krasovskii functional (LKF), a delay-dependent stability criterion is derived for the open-loop fuzzy systems. In the derivation process, some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation, and among the terms in the Leibniz-Newton formula. Then, a delay-dependent stabilization condition based on the so-called parallel distributed compensation (PDC) scheme is worked out for the closed-loop fuzzy systems. The proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities (LMIs) and compared with the existing ones via two examples. Finally, application to control of a truck-trailer is also given to illustrate the effectiveness of the proposed design method.  相似文献   

15.
Cheng-De  Lai-Bing  Zhan-Shan   《Neurocomputing》2009,72(13-15):3331
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.  相似文献   

16.
针对加性时变时滞不确定神经网络的时滞相关鲁棒耗散性问题,提出了一种更一般化的激活函数。与以往研究不同,充分考虑了关于神经元激活函数和加性时变时滞的充分信息,通过使用一些新的积分项构造合适的Lyapunov-Krasovskii泛函(LKF),并利用新生成的单积分不等式来计算其导数,包括延森不等式和维特林积分不等式的特殊情形。利用线性矩阵不等式(LMI)技术建立了一个新的时滞相关的不守恒全局渐近稳定性和耗散准则。最终通过计算和数值仿真验证了所提理论的有效性。  相似文献   

17.
This paper is concerned with the absolute and robust stability for a class of neutral-type Lur'e systems with an interval time-varying delay and sector-bounded nonlinearity. By discretising the delay interval into two segmentations with an unequal width, new delay-dependent sufficient conditions for the absolute and robust stability of neutral-type Lur'e systems are proposed in terms of linear matrix inequalities (LMIs) by employing a modified Lyapunov-Krasovskii functional (LKF). These conditions reduce the conservativeness in computing the maximum allowed delay bounds (MADBs) in many cases. Finally, several standard numerical examples are presented to show the effectiveness of the proposed approach.  相似文献   

18.
This paper is concerned with improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by means of a new (m,N)-delay-partitioning approach. Based on an appropriate augmented LKF established in the framework of state vector augmentation, some tighter bounding inequalities (Seuret-Wirtinger’s integral inequality, Peng-Park’s integral inequality and the reciprocally convex approach) have been employed to deal with (time-varying) delay-dependent integral items of the derivative of LKF, therefore, less conservative delaydependent stability criteria can be obtained on account of none of any useful time-varying items are arbitrarily ignored. It’s worth mentioning that, when the delay-partitioning number m is fixed, less conservatism can be achieved by increase of another delay-partitioning number N, but without increasing any computing burden. Finally, one numerical example is provided to show that the proposed conditions are less conservative than existing ones.  相似文献   

19.
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...  相似文献   

20.
This correspondence studies stability analysis and stabilization for discrete-time Takagi and Sugeno fuzzy systems with state delay. First, a new fuzzy Lyapunov-Krasovskii functional (LKF) is constructed to derive a delay-dependent stability condition for open-loop fuzzy systems. Then, a delay-dependent stabilization approach based on a nonparallel distributed compensation scheme is provided for closed-loop fuzzy systems. Both state feedback and observer-based control cases are considered. The proposed stability and stabilization conditions are represented in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.  相似文献   

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