非线性不平衡弹性轴系动力学的安全裕度准则

给出了一个弹性转子系统的非线性动力学安全裕度准则.采用分解和聚合的方法将系统的积分空间与观察空间分离,在积分空间中得到高维系统的稳态轨迹;根据转子系统振动的国际标准确定安全准则的能量界限,在一系列观察空间中采用能量相比正面积准则计算安全裕度.给出了滑动轴承非线性油膜力条件下不平衡转子系统安全裕度计算的实例.所建议的安全裕度准则包括了工程中通用的稳定裕度的计算,它是解决非线性系统安全裕度和稳定裕度量化计算问题的一种有效方法.     

Strongly absolute stability of Lur'e type differential-algebraic systems

In this paper, we consider Lur'e type differential-algebraic systems (LDS) and introduce the concept of strongly absolute stability. Such a notion is a generalization of absolute stability for Lur'e type standard state-space systems (LSS). By a Lur'e type Lyapunov function, we derive an LMI based stability criterion for LDS to be strongly absolutely stable. Using extended strictly positive realness (ESPR), we present the frequency-domain interpretation of the obtained criterion, by which we simplify the criterion and show that the criterion is a generalization of the well-known Popov criterion. Finally, we illustrate the effectiveness of the main results by a numerical example.     

The drucker stability of a material

An invariant formulation of the criterion for the stability of a material, which enables one to investigate the local stability under arbitrary stress conditions, is obtained on the basis of Drucker's postulate [1]. It is shown that the criterion obtained has an explicit physical meaning at large plastic deformations. A relation is established between the stability parameter and other fundamental parameters of the stressed state.     

Linear stability of a system of Gauss vortices

The stability problems are studied of the rigid body rotation of a regular polygonal system of pointwise and Gauss vortices. A stability criterion is obtained for a system of Gauss vortices which generalizes an available criterion for stability of the rigid body rotation of a system of pointwise vortices. The influence of dispersion of the vorticity distribution on stability of rigid body rotation is studied. It is shown, that there is some finite value of dispersion whose achievement yields the stabilization of known unstable perturbations.     

Nonlinear Stability of General Linear Methods

This paper is devoted to a study of stability of general linear methods for the numerical solution of nonlinear stiff initial value problems in a Hilbert space. New stability concepts are introduced. A criterion of weak algebraic stability is established, which is an improvement and extension of the existing criteria of algebraic stability.     

A new development for the Tikhonov Theorem in nonlinear singular perturbation systems

This paper deals with the exponential stability of nonlinear perturbation systems under a new condition. A novel criterion of exponential stability of nonlinear systems is firstly given in a general form. In this criterion, a new kind of characteristic value is introduced, which makes the exponential stability measurable. Based on this criterion, a new development for the Tikhonov Theorem in nonlinear singular perturbation systems is presented.     

Global exponential stability for a class of neural networks

In this paper, the global exponential stability for a class of neural networks is investigated. A simple criterion ensuring global exponential stability is established, which is a less restrictive version of a recent criterion due to Park and Kwon. Some examples showing the effectiveness of the present criterion are given.     

Improved delay-dependent stability criterion for neural networks with time-varying delay

In this paper, the problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay has been considered. A new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

A novel criterion for delayed feedback control of time-delay chaotic systems

This paper investigated stability criterion of time-delay chaotic systems via delayed feedback control (DFC) using the Lyapunov stability theory and linear matrix inequality (LMI) technique. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is given to illuminate the design procedure and advantage of the result derived.     

Novel criterion for stability of discrete-time systems in a state-space realization utilizing saturation nonlinearities

A new criterion for the global asymptotic stability of discrete-time systems in a state-space realization utilizing saturation nonlinearities is presented. The form of the criterion is unconventional in that it offers the flexibility of using even an unsymmetric Lyapunov matrix P. A recently reported criterion is shown to be a special case of the present criterion. An example shows the effectiveness of the new criterion.     

Absolute stability criteria for infinite-dimensional discrete Lur'e systems with application to loaded distortionless electric RLCG-transmission line

We study absolute stability of a class of discrete Lur'e control system on an infinite-dimensional Hilbert space. Counterparts of the circle criterion and the Szegö criterion are derived using, respectively, quadratic and non-quadratic Lyapunov functionals. A link with existing finite-dimensional theory of absolute stability is shown. The results are illustrated by an example of the loaded distortionless electric RLCG-transmission line with a nonlinear static feedback. Its stability was previously investigated using the circle criterion for continuous infinite-dimensional systems with unbounded control and observation in the frame of systems in factor form.     

Stability of reaction-fronts in porous media

The stability of reaction-fronts in porous media is studied with analytical and numerical methods. A stability criterion has been derived using linear stability analysis assuming a sharp font. The sharp front assumption is an approximation of the mathematical model in the limit of an infinite rapid reaction. The criterion shows that the stability of a sharp reaction front is dependent on the permeability that develops behind it. The sharp front is unstable for perturbations of any wave-length if the permeability increases behind the front. The criterion shows that short wave-length perturbations are more unstable than long wave-length perturbations. The sharp front is labile when the permeabilities are the same at both sides of the front. This means that the perturbed front moves unchanged forward. Finally, perturbations will die out in case the permeability decreases behind the sharp front. The stability of non-sharp fronts are simulated numerically when dissolution is by first order kinetics, the transport is by convection and diffusion and when the permeability and specific reactive surface depends on the porosity. The numerical experiments behave according to the stability criterion.     

Stable odd solutions of some periodic equations modeling satellite motion

A new stability criterion is proved for second-order differential equations with symmetries in terms of the coefficients of the expansion of the nonlinearity up to the third order. Such a criterion provides solutions of twist type, which are Lyapunov-stable solutions with interesting dynamical properties. This result is connected with the existence of upper and lower solutions of a Dirichlet problem and applied to a known equation which model the planar oscillations of a satellite in an elliptic orbit, giving an explicit region of parameters for which there exists a Lyapunov-stable solution.     

Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities

This paper considers the problem of global asymptotic stability of a class of nonlinear uncertain discrete-time state-delayed systems. The class of systems under investigation involves multiple state delays, norm-bounded parameter uncertainties, and generalized overflow nonlinearities which cover usual types of overflow arithmetic used in practice. A new criterion for the global asymptotic stability of such systems is presented. A numerical example is given to illustrate the applicability of the criterion presented.     

Global stability for discrete Cohen–Grossberg neural networks with finite and infinite delays

In this paper, the global stability problem for a general discrete Cohen–Grossberg neural network with finite and infinite delays is investigated. A simple criterion ensuring the global asymptotical stability is established, by applying the Lyapunov method and graph theory. Finally, an example showing the effectiveness of the provided criterion is given.     

Improved global exponential stability for delay difference equations with impulses

In this paper, by means of constructing an impulsive delay difference inequality, we study the global exponential stability for a class of delay difference equations with impulses. A new criterion ensuring the global exponential stability of the equilibrium point is obtained, which is less restrictive and conservative than that given in the earlier reference. An illustrative example is given to demonstrate the effectiveness and advantage of the obtained result.     

时变时滞BAM神经网络系统的指数稳定性分析

利用Lyapunov稳定性理论和线性矩阵不等式技术,得到了保证时变时滞BAM神经网络系统指数稳定性的时滞依赖稳定性准则.所给的准则可用Matlab中的LMI控制工具箱进行验证.仿真实例进一步说明了结果的有效性.     

Improved stability criterion and output feedback control for discrete time-delay systems

This paper investigates the stability and stabilization for a class of linear systems with time-varying delay. We provide a new finite-sum inequality which is a powerful tool for stability analysis of time-delay systems. Applying the inequality, a new stability criterion is proposed in terms of linear matrix inequalities (LMIs). We also design a method for static output feedback (SOF) control problems which contains two parts. The first part is to find an initial values of the matrix variables. By utilizing the initial values, the condition for SOF control problems can be solved by an improved path-following method. Numerical examples demonstrate the effectiveness of the stability criterion and the SOF stabilization method.     

Viscous-inviscid model for the linear stability of core-annular flow

In this paper the linear stability of two immiscible fluids of widely different kinematic viscosity and equal density flowing through a circular pipe is analysed. A viscous-inviscid model is used which offers a consistent zeroth-order approximation to the stability problem as long as the thickness of the ring flow, where the inviscid fluid is located, is large enough. In this way the laminar sublayer at the pipe wall does not interact with the fluid interface. A closed form expression for the complex dispersion relation due to an arbitrary wavelength perturbation is derived, which determines a stability criterion, and then simplified for large and short wavelength values.     

First-passage time for stability analysis of the Kaldor model

Every economic model should include an estimate of its stability and predictability. A new measure, the first passage time (FPT) which is defined as the time period when the model error first exceeds a pre-determined criterion (i.e., the tolerance level), is proposed here to estimate the model predictability. A theoretical framework is developed to determine the mean and variance of FPT. The classical Kaldor model is taken as an example to show the robustness of using FPT as a quantitative measure for identifying the model stability.