Exponential stability analysis for uncertain switched neutral systems with interval-time-varying state delay

The global exponential stability for a class of switched neutral systems with interval-time-varying state delay and two classes of perturbations is investigated in this paper. LMI-based delay-dependent and delay-independent criteria are proposed to guarantee exponential stability for our considered systems under any switched signal. The Razumikhin-like approach and the Leibniz–Newton formula are used to find the stability conditions. Structured and unstructured uncertainties are studied in this paper. Finally, some numerical examples are illustrated to show the improved results from using this method.     

On the stability of characterization of the normal distribution by the properties of linear forms

If the assumptions of the characterization theorem are fulfilled not exactly but only approximately, then can we state that the conclusion of this characterization is also fulfilled approximately? Theorems in which this kind of problems are considered are called stability theorems or the stability of characterizations. The problems of the stability of characterization of the normal distribution by means of identically distributed linear form and monomial are considered in a uniform metric. The moment and symmetry conditions are considerably weaker in comparison to previously published versions of the theorem. The choice of a uniform metric appears to be very natural in the framework of Zolotarev’s methodology advising to investigate stability.     

Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay

The switching signal (switching law) design for robust global exponential stability of switched nonlinear systems is investigated in this paper. LMI-based delay-dependent criteria are proposed to design the switching signal and guarantee the global exponential stability. Free weighting matrix and additional nonnegative inequality approaches are used in this paper to find the less conservative stability results. Finally, some numerical examples are illustrated to show the main improvement.     

Stability of delayed cellular neural networks

Global asymptotic stability and exponential stability of delayed cellular neural networks is considered in this paper. Based on the Lyapunov stability theorem as well as a fact about the elemental inequality, some new sufficient conditions are given for global asymptotic stability and exponential stability of delayed cellular neural networks. The results are less conservative than those established in the earlier references. Three examples are given to illustrate the applicability of these conditions.     

Oscillation and stability of nonlinear neutral impulsive delay differential equations

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equation are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.     

二元稳定网络的算法及模型

通过建立JW(Jackson-Wolinsky)规则之下二元稳定网络的等价条件, 给出其完整算法. 引入边支付后, 证明了增连接情形具有边支付的二元稳定网络集合是二元稳定网络集合与具有边支付的二元稳定网络集合的交集. 考察两个特定的网络模型, 系统分析了它们的二元稳定性.     

Stability of Local Efficiency in Multiobjective Optimization

Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we define a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufficient conditions on when strict locally efficient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions.     

Stability analysis for variational inequality in reflexive Banach spaces

This paper is devoted to the stability analysis in variational inequality. We obtain some stability results for variational inequality with both the mapping and the set that are perturbed in reflexive Banach spaces, provided that the mappings are pseudomonotone in the sense of Karamardian. The stability is also discussed for the Minty variational inequality as the mappings are properly quasimonotone. The results in this paper generalized some known results in this area.     

Stability of impulsive functional differential equations

In this paper the stability of impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied. By using Lyapunov functions and Razumikhin techniques, some criteria of stability, asymptotic stability and practical stability for impulsive functional differential equations in which the state variables on the impulses are related to the time delay are provided. Some examples are also presented to illustrate the efficiency of the results obtained.     

Stability andB-convergence of linearly implicit Runge-Kutta methods

Summary In this paper we study stability and convergence properties of linearly implicit Runge-Kutta methods applied to stiff semi-linear systems of differential equations. The stability analysis includes stability with respect to internal perturbations. All results presented in this paper are independent of the stiffness of the system.     

Stability analysis of uncertain fuzzy Hopfield neural networks with time delays

In this paper, the global stability problem of uncertain Takagi–Sugeno (T–S) fuzzy Hopfield neural networks with time delays (TSFHNNs) is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSFHNNs. Here, we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain generalized stability region. In fact, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. The proposed stability conditions are demonstrated with four numerical examples. Comparison with other stability conditions in the literature shows our conditions are the more powerful ones to guarantee the widest stability region.     

Liapunov asymptotic stability and Zhukovskij asymptotic stability

In this paper the Liapunov stability and Zhukovkij stability of motion in continuous dynamical systems are discussed. It is shown that each type of asymptotic stability is typically characterized by omega limit set of an orbit of this type of stability.     

关于趋化性的O-S型方程定态解的稳定性

本文利用由线性逼近得到稳定性的相关理论,通过对平衡点进行稳定性分析,讨论了一类趋化性方程常定态的稳定性.文中给出了相应的稳定性判别准则,并将这些结果应用于一些重要的生物模型.     

ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL

In 1994, Grove, Kocic, Ladas, and Levin conjectured that the local stability and global stability conditions of the fixed point y = 1/2 in the genotype selection model should be equivalent. In this article, we give an affirmative answer to this conjecture and prove that local stability implies global stability. Some illustrative examples are included to demonstrate the validity and applicability of the results.     

脉冲耦合时滞微分与连续差分系统的稳定性

该文研究脉冲耦合时滞微分与连续差分系统的稳定性.首先,该文为这类系统引入了一些新的概念如L_2稳定、吸引和L_2渐近稳定,然后给出了一些系统L_2稳定和L_2渐近稳定的判据.该文也给出了一个例子来验证所得结论的有效性.应该注意到这是首次考虑这类脉冲系统.     

New stability criteria for a class of neutral systems with discrete and distributed time-delays: an LMI approach

In this paper, a problem of the asymptotic stability for a class of neutral systems with multiple discrete and distributed time-delays is considered. Lyapunov stability theory is applied to guarantee the stability for the systems. New discrete-delay-independent and discrete-delay-dependent stability conditions are derived in terms of the spectral radius and linear matrix inequality. By mathematical analysis, the stability criteria are proved to be less conservative than the ones reported in the current literatures. A numerical example is given to illustrate the availability of the proposed results.     

三维Boussinesq方程组大解的全局L~2稳定性

对三维有界及无界区域上的Boussinesq方程的全局L~2稳定性进行了讨论.在解满足适当的条件下,证明了此解为稳定的,并得出此稳定性条件的等价性条件,最后得出了二维Boussinesq方程组在三维扰动下的解的全局存在性和稳定性.     

Exponential stability criteria of uncertain systems with multiple time delays

The exponential stability (with convergence rate α) of uncertain linear systems with multiple time delays is studied in this paper. Using the characteristic function of linear time-delay system, stability criteria are derived to guarantee α-stability. Sufficient conditions are also obtained for exponential stability of uncertain parametric systems with multiple time delays. For two-dimensional time-invariant system with multiple time delays, the proposed stability criteria are shown to be less conservative than those in the literature. Numerical examples are given to illustrate the validity of our new stability criteria.