On Global Asymptotic Stability of Cohen–Grossberg Neural Networks With Variable Delays

This paper studies the problems of existence, uniqueness, global asymptotic stability and global exponential stability of the equilibrium of Cohen-Grossberg neural networks with variable delays. An estimation technique based on delay differential inequality with variable coefficients is developed to establish delay-independent/delay-dependent sufficient conditions for global asymptotic/exponential stability. The stability criteria obtained are based on the $M$-matrix theory. These criteria can be easily checked in practice and do not require that the delays be constant or differentiable. In particular, our delay-independent asymptotic/exponential stability criteria remove a restriction on the amplification functions imposed by the existing results. Furthermore, our delay-dependent exponential stability criteria give explicitly the allowable upper bound on the diagonal delays such that the global stability property of Cohen-Grossberg neural networks can be retained. Thus, our new results are of great importance in design and application of Cohen-Grossberg neural networks with variable delays. The effectiveness of the new results is further illustrated by two numerical examples in comparison with the existing results.      

Delay-Dependent Exponential Stability of Neural Networks With Variable Delay: An LMI Approach

This brief focuses on the problem of delay-dependent stability analysis of neural networks with variable delay. Two types of variable delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing a new type of Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for exponential stability of delayed neural networks are derived in terms of linear matrix inequalities. We also obtain delay-independent stability criteria. Two examples are presented which show our results are less conservative than the existing stability criteria.     

Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays

This paper provides new delay-dependent conditions that guarantee the robust exponential stability of stochastic Hopfield type neural networks with time-varying delays and parameter uncertainties. Both the cases of the time-varying delays which are differentiable and may not be differentiable are considered. The stability conditions are derived by using the recently developed free-weighting matrices technique and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria. It is shown that the proposed stability results are less conservative than some previous ones in the literature.      

基于LMI的时变时滞Cohen-Grossberg神经网络鲁棒稳定性

 研究了时变时滞Cohen-Grossberg神经网络的全局鲁棒稳定性问题.基于线性矩阵不等式技术,给出了保证时变时滞Cohen-Grossberg神经网络平衡点唯一性和全局鲁棒稳定性的新判据.这些新判据不依赖于时滞的大小和放大函数,且与现有的一些结果相比,具有易于验证、适用范围广、条件更不保守等特点.仿真结果验证了本文方法的有效性.     

An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis

In this paper, using a method based on nonsmooth analysis and the Lyapunov method, several new sufficient conditions are derived to ensure existence and global asymptotic stability of the equilibrium point for delayed Cohen-Grossberg neural networks. The obtained criteria can be checked easily in practice and have a distinguished feature from previous studies, and our results do not need the smoothness of the behaved function, boundedness of the activation function and the symmetry of the connection matrices. Moreover, two examples are exploited to illustrate the effectiveness of the proposed criteria in comparison with some existing results.     

Global asymptotic stability of delayed Cohen-Grossberg neural networks

In this paper, we study the Cohen-Grossberg neural networks with discrete and distributed delays. For a general class of internal decay functions, without assuming the boundedness, differentiability, and monotonicity of the activation functions, we establish some sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability. Theory of M-matrices and Lyapunov functional technique are employed. The criteria are independent of delays and hence delays are harmless in our case. Our results improve and generalize some existing ones.     

Sufficient Conditions for Convergence of the Sum–Product Algorithm

Novel conditions are derived that guarantee convergence of the Sum-Product Algorithm (also known as Loopy Belief Propagation or simply Belief Propagation (BP)) to a unique fixed point, irrespective of the initial messages, for parallel (synchronous) updates. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. The conditions are compared with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, sufficient conditions are derived that take into account local evidence (i.e., single-variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds.      

Complete stability of cellular neural networks with time-varying delays

In this paper, the complete stability of cellular neural networks with time-varying delays is analyzed using the induction method and the contraction mapping principle. Delay-dependent and delay-independent conditions are obtained for locally stable equilibrium points to be located anywhere, which differ from the existing results on complete stability where the existence of equilibrium points in the saturation region is necessary for complete stability and locally stable equilibrium points can be in the saturation region only. In addition, some existing stability results in the literature are special cases of a new result herein. Simulation results are also discussed by use of two illustrative examples.     

A New Stability Criterion for a Partial Element Equivalent Circuit Model of Neutral Type

This brief is concerned with stability for a partial element equivalent circuit model of neutral type. First, the relationship between two recently established integral inequalities is presented. Second, a new Lyapunov-Krasovskii functional is introduced based on the fact that the delay interval is nonuniformly divided into multiple subintervals, and different functionals are chosen on different subintervals. Then, some new delay-dependent criteria are derived. Finally, a numerical example is given to show that the results obtained by the new stability criteria can significantly improve some existing results.     

Exponential Stability of Impulsive Delayed Linear Differential Equations

This brief considers the global exponential stability of impulsive delayed linear differential equations. By utilizing the Lyapunov function methods combined with the Razumikhin technique, several criteria on exponential stability are analytically derived, which are substantially an extension and a generalization of the corresponding results in recent literature. Compared with some existing works, a distinctive feature of this brief is to address exponential stability problems for any fixed-time delays. It is shown that the delayed linear differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. An example and its simulation are also given to illustrate the theoretic results.     

Design and Stability Criteria of Networked Predictive Control Systems With Random Network Delay in the Feedback Channel

This paper is concerned with the design of networked control systems (NCSs) with random network delay in the feedback channel and gives stability criteria of closed-loop networked predictive control systems. The principle of predictive control is adopted to overcome the effects of network time delay. The necessary and sufficient conditions on the stability of the closed-loop NCS are derived, which provides useful analytical stability criteria. The closed-loop networked predictive control system with bounded random network delay is stable if the corresponding switched system is stable. Simulation and real-time results give an illustration of the proposed control strategies     

离散Hopfield神经网络的稳定性研究

离散Hopfield神经网络的稳定性是网络应用的基础.文中主要研究非对称离散Hopfield神经网络的异步、同步、部分同步演化方式的稳定性,并给出了一些新的稳定性条件,所获结果推广了一些已有的结论.     

Mean Square Exponential Stability for Uncertain Delayed Stochastic Neural Networks with Markovian Jump Parameters

This paper is concerned with the problem of delay-dependent mean square exponential stability for a class of delayed stochastic Hopfield neural networks with Markovian jump parameters. The delays here are time-varying delays. Based on a new Lyapunov–Krasovskii functional, delay-dependent stability conditions are derived by means of linear matrix inequalities (LMIs). It is shown that the proposed results can contain some existing stability conditions as a special case. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method, and the simulations show that our results are less conservative than the existing ones.     

Novel Delay-Dependent Stability Criteria for Fuzzy Neural Networks Using Delay-Decomposition Approach

This paper investigates the global asymptotic stability of fuzzy neural networks with time-varying and unbounded continuously distributed delays in mean square. Based on a new Lyapunov–Krasovskii functional, by effective combination of Jensen integral inequality with reciprocally convex and quadratic convex combination method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which are expressed in terms of linear matrix inequalities, can be easily verified via MATLAB software. The main advantage of the proposed criteria lies in its reduced conservatism by means of the time delay-decomposition technique and Wirtinger-based inequality. In addition to that, a numerical example is given to demonstrate the effectiveness and less conservativeness of our theoretical results over the existing literature.     

Necessary and Sufficient Conditions for the Stability of Microwave Amplifiers With Variable Termination Impedances

New criteria to check conditional stability of microwave amplifiers with input and output terminations varying in pre-specified circular regions surrounding complex nominal values are proposed. Necessary and sufficient conditions are provided both in terms of the immittance parameters$lambda_ ij$(i.e.,$ z_ ij, y_ ij, g_ ij,$or$ h_ ij$) and in terms of the scattering parameters$ s_ ij$. Proposed conditions can be easily implemented in any commercial computer-aided design tool and are suitable to be used as design goals within an optimization routine: this allows to optimize the tradeoff between stability constraints under termination variations and performance in a yield-oriented design flow. A case study, in which a distributed amplifier has been designed, shows the advantages of the proposed approach.     

Delay-Dependent H∞ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays

This paper deals with the problems of delay-dependent robust H_infin control and filtering for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian delay systems are obtained by introducing some slack matrix variables. The conservatism caused by either model transformation or bounding techniques is reduced. Based on the proposed BRL, sufficient conditions for the solvability of the robust H_infin control and H_infin filtering problems are proposed, respectively. Dynamic output feedback controllers and full-order filters, which guarantee the resulting closed-loop system and the error system, respectively, to be stochastically stable and satisfy a prescribed H_infin performance level for all delays no larger than a given upper bound, are constructed. Numerical examples are provided to demonstrate the reduced conservatism of the proposed results in this paper.     

Synchronization in Complex Dynamical Networks With Random Sensor Delay

This brief proposes a new complex dynamical network model, in which nodes are connected by measured outputs experiencing the random sensor delay. This model is totally different from some existing network models. Then, synchronization in the proposed network model is analyzed by the stochastic stability theory. A sufficient synchronization condition is given to ensure that the proposed network model is exponentially mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.      

Robust Stability of Uncertain Discrete Impulsive Systems

This brief studies uncertain discrete impulsive systems. The robustly asymptotical stability criteria are established for linear discrete impulsive system and a class of uncertain nonlinear discrete impulsive systems, respectively. These stability criteria are expressed in terms of fairly simple algebraic conditions so that they are easy to be tested. Some examples are given to illustrate results obtained by us     

Improved Sufficient Conditions for Global Asymptotic Stability of Delayed Neural Networks

This brief addresses the global asymptotic stability (GAS) of delayed neural networks. Based on the Lyapunov method, using some existing results for the existence and uniqueness of the equilibrium point, some sufficient conditions are obtained for checking the GAS without demanding the boundedness and differentiability hypotheses for activation functions. Through comparison, it is illustrated that our conditions extend and improve some recent results.     

Stability Criteria for Impulsive Systems With Time Delay and Unstable System Matrices

This paper studies stability problems of a class of impulsive systems with time delay whose linear parts contain unstable system matrices. By using the method of variation of parameters, Lyapunov functions and inequalities, several stability criteria are established for both linear and nonlinear impulsive systems with time delay. It is shown that the time delay systems can be stabilized by impulses even if the system matrices are unstable. Several numerical examples are given to illustrate the results.