The Asymptotic Stability for a Class of Nonlinear Large Sceale System

This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.

A LOWER BOUND OF STABLE STATIONARY TRAJECTORIES

It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.

STABLE AND UNSTABLE STATIONARY TRAJECTORIES

The stability of stationary trajectories of a particular autonomous system is studied.The proof of the result is based upon continuation methods.

DYNAMICS OF A NONLINEAR NON-AUTONOMOUS n-PATCHES PREDATOR-PREY DISPERSION-DELAY MODEL

In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved that the system is uniformly persistent under any dispersion rate effect. Furthermore~ some sufficient conditions are established for the existence of a unique almost periodic solution of the system. The example shows that the criteria in the paper are new, general and easily verifiable.

Stochastic stabilization analysis of networked control systems

Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.

Consensus protocol for multi-agent continuous systems

Based on the algebraic graph theory, the networked multi-agent continuous systems are investigated. Firstly, the digraph （directed graph） represents the topology of a networked system, and then a consensus convergence criterion of system is proposed. Secondly, the issue of stability of multi-agent systems and the consensus convergence problem of information states are all analysed. Furthermore, the consensus equilibrium point of system is proved to be global and asymptotically reach the convex combination of initial states. Finally, two examples are taken to show the effectiveness of the results obtained in this paper.

The Stability for the Hyperneutral Type Nonlinear Time Varying Control Systems(1)

We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization.Making use of the symmetric positive definite solution of Riccati matrix differential equation which corresponds to the linear time varying control system, we construct the Lyapunov function.Then we provide the sufficent conditions which make that the zero solution of the hyperneutral type nonlinear time varying control systems is uniformly asymptotically stable by means of the Lyapunov equivalence decomposition method, and find the formulaes which can be used to estimate the bounds of the time delays and the nonlinear terms.

A Kind of Predator-prey System of Holling Type II and Interaction Perturbation with Impulsive Effect

A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.

On the model-based networked control for singularly perturbed systems

In this paper, the control of a two-time-scale plant, where the sensor is connected to a linear controller/ actuator via a network is addressed. The slow and fast systems of singularly perturbed systems are used to produce an estimate of the plant state behavior between transmission times, by which one can reduce the usage of the network. The approximate solutions of the whole systems are derived and it is shown that the whole systems via the network control are generally asymptotically stable as long as their slow and fast systems are both stable. These results are also extended to the case of network delay.

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.

IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS

Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.

The Lotka-Volterra Competition System with Discrete and Distributed Time Delays

In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don＇t effect the stability of the equilibrium in the delay system. Finally, we can conclude that the positive equilibrium is global asymptotically stable in the delay system.

Global Dynamics of a Predator-prey Model

In this paper, we consider a predator-prey model. A sufficient conditionis presented for the stability of the equilibrium, which is different from the one for themodel with Hassell-Varley type functional response. Furthermore, by constructing aLyapunov function, we prove that the positive equilibrium is asymptotically stable.

Periodic Solutions of a Cooperative System with State Feedback Control

In this paper, we propose a semi-continuous dynamical system to study the cooperative system with feedback control. Based on geometrical analysis and the analogue of Poincare criterion, the existence and stability of the positive order one periodic solutions are given. Numerical results are carried out to illustrate the feasibility of our main results.

STABILITY OF THE BURGERS SHOCK WAVE

This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance. It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.

BIBO Stability of Continuous Time Systems

In this paper, the problems of the stability analysis and BIBO stabilization for the switched systems are considered. Applying a stabilizing local state feedback to each subsystem, the sufficient conditions of the asymptotically stable and BIBO stabilization for the switched systems are obtained by means of the method of Lyapunov function and the method of inequality analysis.

THE STABILITY OF A KIND OF DISCRETE-TIME HOPFIELD NEURAL NETWORKS WITH ASYMPTOTICAL WEIGHTED MATRICES

In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale＇s invariance principle in difference equation is applied.

Fixed Point and Asymptotical Stability in p-Moment of Neutral Stochastic Differential Equations with Mixed Delays

In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.

STABILITY OF SOLUTIONS OF FIRST ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH OSCILLATORY COEFFICIENTS

This paper discusses a class of first order nonlinear neutral equations. The asymptotic behavior of the nonoscillatory solutions and the oscillatory solutions of the equations are discussed. Sufficient conditions for the asymptotic stability of the trivial solutions of the equations are obtained.

ALMOST PERIODIC SOLUTION OF TWO－SPECIES PATCHTYPE NONAUTONOMOUS DIFFUSIVE LOTKA－VOLTERRA COMPETITIVE MODELS

In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot diffuse. We prove that the systems can have aunique positive almost periodic solution, which is globally uniformly asymptotically stableunder some appropriate conditions. In particular, if the system is a periodic system of period ω, it can have a positive globally uniformly asymptotically stable periodic solution ofperiod ω, which is a generalization of Theorem 4 in paper [6].