On the Stability of Globally Projected Dynamical Systems

Two types of projected dynamical systems, whose equilibrium states solve the corresponding variational inequality problems, were proposed recently by Dupuis and Nagurney (Ref. 1) and by Friesz et al. (Ref. 2). The stability of the dynamical system developed by Dupuis and Nagurney has been studied completely (Ref. 3). This paper analyzes and proves the global asymptotic stability of the dynamical system proposed by Friesz et al. under monotone and symmetric mapping conditions. Furthermore, the dynamical system is shown to be globally exponentially stable under stronger conditions. Finally, we show that the dynamical system proposed by Friesz et al. can be applied easily to neural networks for solving a class of optimization problems.     

On the Stability of Invariant Sets of Discontinuous Dynamical Systems

We establish sufficient conditions for the stability, asymptotic stability, and instability of invariant sets of discontinuous dynamical systems.     

一类离散动力系统的稳定性

研究一类作 为基因选择模 型的离散动力系 统ｙ ｎ ＋ １ ＝ ｙｎ ｅｂ（ １ － ２ ｙ ｎ － ｋ ）１－ ｙｎ ＋ ｙｎ ｅｂ（ １ － ２ ｙ ｎ － ｋ ） ,　ｎ ＝ ０,１,… ,的稳定性 ,其中 ｂ∈（０,∞）, Ｋ∈ ｛１,２,…｝     

动力系统中的Lipschitz稳定性

本文讨论动力系统的Ｌｉｐｓｃｈｉｔｚ稳定性与吸引性之间的关系．给出动力系统中弱吸引性、吸引性和强吸引性这三个概念相互等价的条件，在一定的条件下证明了（弱、强）吸引子与全局（弱、强）吸引子是一致的．本文还讨论了度量Ｌｙａｐｕｎｏｖ稳定性和拓扑Ｌｙａｐｕｎｏｖ稳定性及它们与Ｌｉｐｓｃｈｉｔｚ稳定性之间的关系．     

一类变系数动力系统的运动稳定性

本文通过引入线性算子L_A,得到无穷矩阵序列{A_k(t)},基于此,讨论由“平均”系统稳定性确定原系统稳定性的条件,得到一些较为广泛的结果,包含了文[1]、[2]的相应结论。特别,对一些特殊类型的二阶系统,得到一些易于验证的直接判据。     

线性广义系统时滞相关渐近稳定的一个新判据

研究线性广义时滞系统时滞相关的渐近稳定性问题.利用Lyapunov-Krasovskii泛函理论和自由权矩阵方法,得到严格线性矩阵不等式(LMI)形式的时滞相关渐近稳定新判据,并没有采用模型变换和界定交叉项方法.最后通过数值算例验证新判据的有效性.     

RESEARCH ANNOUNCEMENTS —— On the conditions for the Orbitally Asymptot

This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system x′=f(x), x Rn , (1) where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability. 　　For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e.     

Asymptotical Stability in Probability for Stochastic Bilinear Systems with Markovian Switching

This paper deals with asymptotical stability in probability in the large for stochastic bilinear systems. Some new criteria for asymptotical stability of such systems have been established in the inequality of mathematic expectation. A sufficient condition for bilinear stochastic jump systems to be asymptotically stable in probability in the large in Markovian switching laws is derived in a couple of Riccati-like inequalities by introducing a nonlinear state feedback controller. An illustrative example shows the effectiveness of the method.     

Stability of Random Dynamical Systems on Banach Spaces

We consider a stochastic process generated by random dynamical systems on Banach spaces. Under the suitable assumptions we show that this process is weakly convergent to some limit.     

Conditional Stability for the Hexagonal Anisotropic Elastic Dynamical Systems

In this paper we prove a conditional stability for the hexagonal anisotropic dynamical elastic systems with smooth coefficients satisfying some conditions. The proof is based on the localized Fourier–Gauss transformation and the three balls inequality for the associated elliptic system.     

Markov切换随机双线性系统依概率渐进稳定性

本文研究随机双线性系统大范围渐进稳定性。利用数学期望不等式给出了随机双线性系统渐进稳定的新标准。设计了一种非线性状态反馈控制器,利用类Riccati不等式推出了Markov切换随机双线性系统大范围依概率渐进稳定的充分条件。数值算例表明本文提出的方法是可行的。     

Criteria for the Asymptotic Stability of Solutions of Dynamical Systems

We present a new proof for criteria for the asymptotic stability of systems of difference and differential equations based on the properties of monotone operators in a semiordered space. We also establish necessary and sufficient conditions for the asymptotic stability of stochastic systems of differential and difference equations in the mean square.     

Stability and Controllability in Non-autonomous Time-discrete Dynamical Systems

In this paper stability and attractivity in non-autonomous time-discrete dynamical systems is investigated with the aid of Lyapunov functions. The results are applied to the problem of stabilization of controlled systems by feedback controls. In the final section of the paper we give sufficient conditions for norm-bounded null-controllability of linear systems.     

Problems of Stability of Dynamical Systems and Computer Algebra

Examples of problems of motion stability solved with the help of computer algebra systems (CAS) are presented. The authors have experience in developing and applying problem-oriented systems of symbolic computations and software packages for solving problems of dynamics of multi-body systems. The algorithms under consideration are implemented (completely or partly) with the aid of up-to-date CAS. They are intended for inclusion in the ``Stability' package of symbolic computation. Bibliography: 6 titles.     

RESEARCH ANNOUNCEMENTS:On the Conditions for the OrbitallyAsymptotical Stability of the AlmostPeriodic Orbits of Dynamical Systems

This paper studies the behaviors of the solutions in the vicinity of a given almost periodicsolution of the autonomous systemwhere f ∈E C1(Rn, Rn). Since the periodic solutions of the autonomous system are not Liapunovasymptotic stable, we consider the weak orbitally stability.For the planar autonomous systems (n=2), the classical result of orbitally stability aboutits periodic solution with period w belongs to Poincare, i.e.Theorem A[1,2] A periodic solution p(t) to (1) with period w is o…     

On Nonlinear Perturbations of Dynamical Systems

The nonlinear variation-of-constants formula is generalizedto the case where the unperturbed operator has nonelliptic Fréchetderivation.     

一类非线性控制系统解的渐近性质

主要目的是研究一类非线性控制系统解的渐近性质。通过建立沿着解的无穷积分和借助于积分形式的LaSalle不变原理,得到了关于系统解的二分性和全局渐近性的判别准则。改进和进一步发展了Айсагалиев所得到的研究方法与结论。