广义连续反馈型神经网络的稳定性

通过对连续Hopfield网络模型的抽象,提出了广义连续反馈型神经网络的概念,指出一种不需要构造能量函数对网络模型的稳定性进行分析和判别的方法,同时给出了相应的数学证明。     

Stability of switching infinite-dimensional systems

In this note, we generalize the results from Narendra and Balakrishnan (IEEE Trans. Automatic Control 39 (1994) 2469) to the infinite-dimensional system theoretic setting. The paper gives results on the stability of a switching system of the form , i∈{1,2}, when the infinitesimal generators A₁ and A₂ commute. In addition, the existence of a common quadratic Lyapunov function is demonstrated.     

FluidSim: a tool to simulate fluid models of high-speed networks

In this paper, we present a tool for the simulation of fluid models of high-speed telecommunication networks. The aim of such a simulator is to evaluate measures which cannot be obtained through standard tools in reasonable time or through analytical approaches. We follow an event-driven approach in which events are associated with rate changes in fluid flows. We show that under some loose restrictions on the sources, this suffices to efficiently simulate the evolution in time of fairly complex models. Some examples illustrate the utilization of this approach and the gain that can be observed over standard simulation tools.     

Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses

In this paper, the robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses is considered. It is assumed that the considered impulsive neural networks have norm-bounded parametric uncertainties and time-varying delays and the state variables on the impulses may relate to the time-varying delays. By using Lyapunov functions together with Razumikhin technique or with differential inequalities, some new robust exponential stability criteria are provided. Some examples and their simulations, including examples that the stability of which can not be tackled by the existing results, are also presented to illustrate the effectiveness and the advantage of the obtained results.     

Stability analysis for a class of switched nonlinear systems

This paper addresses the stability analysis of a class of switched nonlinear systems. The switched systems have uncertain nonlinear functions constrained in a sector set, which are called admissible sector nonlinearities. A sufficient condition in terms of linear inequalities is presented to guarantee the existence of a common Lyapunov function, and thereby to ensure that the switched system is stable for an arbitrary switching signal and any admissible sector nonlinearities. A constructive algorithm based on the modified Gaussian elimination procedure is given to find the solutions of the linear inequalities. The obtained results are applied to a population model with switchings of parameter values and the conditions of ultimate boundedness of its solutions are investigated. Another example of an automatic control system is considered to demonstrate the effectiveness of the proposed approaches.     

Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions

This paper investigates the global asymptotic stability of the periodic solution for a general class of neural networks whose neuron activation functions are modeled by discontinuous functions with linear growth property. By using Leray-Schauder alternative theorem, the existence of the periodic solution is proved. Based on the matrix theory and generalized Lyapunov approach, a sufficient condition which ensures the global asymptotical stability of a unique periodic solution is presented. The obtained results can be applied to check the global asymptotical stability of discontinuous neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also conform the validity of Forti’s conjecture for discontinuous neural networks with linear growth activation functions. Two illustrative examples are given to demonstrate the effectiveness of the present results.     

Stability analysis for coupled systems of fractional differential equations on networks

This paper considers the stability problem for some coupled systems of fractional differential equations on networks (CSFDENs). We provide a systematic method for constructing a Lyapunov function for CSFDENs by using graph theory and the Lyapunov method. Consequently, some sufficient conditions for stability, uniform stability and uniform asymptotic stability of CSFDENs are obtained. Finally, an example and some numerical simulations are presented to verify the effectiveness of the theoretical results.     

非线性时变系统的稳定性

研究非线性时变系统的稳定性问题。通过引入具有齐次导数的时不变Lyapunov函数和近似系统的概念，给出一般非线性时变系统的零解渐近稳定的两个充分条件。应用实例显示出所给出方法在应用中是有效和方便的。     

随机时滞神经网络的全局指数稳定性

首先对一般随机系统的渐近特性进行了讨论.然后结合神经网络的特点,应用李雅普诺夫第二方法对一类随机时滞神经网络系统的全局指数稳定性进行了分析,给出了易于判定随机时滞神经网络几乎必然指数稳定性新的代数判据,并给出实例进行仿真实验.     

Transient analysis of stochastic fluid models

We analyze the transient behavior of stochastic fluid flow models in which the input and output rates are controlled by a finite homogeneous Markov process. Such models are used in asynchronous transfer mode (ATM) to evaluate the performance of fast packet switching and in manufacturing systems for the performance of producers and consumers coupled by a buffer. The transient analysis of such models has already been considered in earlier works and solutions have been obtained by the use of Laplace transform. We derive in this paper a new transient solution only based on recurrence relations. We show that this solution is particularly interesting for its numerical properties. The limiting behavior of the solution is also considered. We empirically show that the algorithm for computing the transient solution can be stopped when some stationary behavior is detected.     

Infinitesimal and finite perturbation analysis for queueing networks

The sample-path perturbation analysis technique is extended to include finite (and possibly large) perturbations typically introduced by changes in queue sizes or other parameters. It is shown that there is a natural hierarchy of perturbation analysis which takes care of increasingly large perturbations. Experiments with zero (infinitesimal) and first order (finite) perturbation analysis show that significant accuracy improvement can be obtained with small increase in computational effort.     

Dissipativity analysis of neural networks with time-varying delays

A new definition of dissipativity for neural networks is presented in this paper. By constructing proper Lyapunov functionals and using some analytic techniques, sufficient conditions are given to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties and the integro-differential neural networks in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the obtained results.     

Novel decentralized adaptive strategies for the synchronization of complex networks

This paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative local adaptive approach. In particular, time-varying feedback coupling gains are considered, whose gradient is a function of the local synchronization error over each edge in the network. It is shown that, under appropriate conditions, the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network. The theoretical derivation is complemented by its validation on a set of representative examples.     

Modeling and stability analysis of cascade buck converters with N power stages

This paper presents a method for stability analysis of N-cell cascade step-down buck converters, which is a kind of complex nonlinear system. A nonlinear model in the form of time-variant state equations is derived, and then the loop gain describing the overall system is introduced. With the help of them, we obtain the equations for phase cross over frequency and gain margin by small-signal perturbation technique, harmonic balance method, and inverse iteration method. Based on the equations, the overall cascade system stability can be analyzed regardless of the number of converters cascaded. Finally, the cascade buck converter with three power stages is used to demonstrate the effectiveness of the proposed stability analysis method.     

On global uniform asymptotic stability of nonlinear time-varying systems in cascade

In this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade. In particular, we give sufficient conditions to guarantee that (i) a globally uniformly stable (GUS) nonlinear time-varying (NLTV) system remains GUS when it is perturbed by the output of a globally uniformly asymptotically stable (GUAS) NLTV system, under the assumption that the perturbing signal is absolutely integrable; (ii) if in addition the perturbed system is GUAS, it remains GUAS under the cascaded interconnection; (iii) two GUAS systems yield a GUAS cascaded system, under some growth restrictions over the Lyapunov function. Our proofs rely on the second method of Lyapunov, roughly speaking on a “δ- stability analysis”.     

采用双交叠模糊分划的T-S模糊系统的稳定性分析

研究前件变量采用双交叠模糊分划的T-S模糊系统的稳定性问题．首先针对自由系统,将连续时间系统的、基于最大交叠规则组的稳定性分析方法推广应用于离散时间系统,并采用模糊Lyapunov方法得到了稳定性的新结论．采用非并行分布补偿控制律,针对受控系统也得到了相应的结论．这些结论比已有的结果更加宽松．仿真例子验证了该稳定性结论．     

Gain margin and Lyapunov analysis of discrete-time network synchronization via Riccati design

This paper deals with solution analysis and gain margin analysis of a modified algebraic Riccati matrix equation, and the Lyapunov analysis for discrete-time network synchronization with directed graph topologies. First, the structure of the solution to the Riccati equation associated with a single-input controllable system is analyzed. The solution matrix entries are represented using unknown closed-loop pole variables that are solved via a system of scalar quadratic equations. Then, the gain margin is studied for the modified Riccati equation for both multi-input and single-input systems. A disc gain margin in the complex plane is obtained using the solution matrix. Finally, the feasibility of the Riccati design for the discrete-time network synchronization with general directed graphs is solved via the Lyapunov analysis approach and the gain margin approach, respectively. In the design, a network Lyapunov function is constructed using the Kronecker product of two positive definite matrices: one is the graph positive definite matrix solved from a graph Lyapunov matrix inequality involving the graph Laplacian matrix; the other is the dynamical positive definite matrix solved from the modified Riccati equation. The synchronizing conditions are obtained for the two Riccati design approaches, respectively.     

Stability analysis of interconnected systems with possibly unstable subsystems

A direct method is presented for stability analysis of nonlinear interconnected dynamical systems. A new scalar Lyapunov function is considered as weighted sum of individual Lyapunov functions for each free subsystem and individual scalar functions related separately to each connection. Sufficient conditions are obtained for asymptotic stability of the equilibrium state by testing the definity of two constant square matrices whose dimension is equal to the number of subsystems. This method can assure stability of systems with possible unstable subsystems. A simple numerical example is included to illustrate this theory.     

Almost sure exponential stability of stochastic cellular neural networks with unbounded distributed delays

In this paper, a cellular neural network whose state variables are governed by stochastic non-linear integro-differential equations is investigated. The considered delays are distributed continuously over unbounded intervals. By applying the Lyapunov functional method, the semimartingale convergence theorem, and some inequality technique, we obtain some sufficient criteria to check the almost sure exponential stability of the system, which generalizes and improves some earlier publications. Two examples are also given to demonstrate our results.