GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function

In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.

Global stabilization for a class of nonlinear time-delay systems using linear output feedback

The stabilization problem via the linear output feedback controller is addressed for a class of nonlinear systems subject to time-delay.The uncertainty of the system satisfies the lower-triangular growth condition and it is affected by time-delay. A linear output feedback controller with a tunable scaling gain is constructed.By selecting an appropriate Lyapunov-Krasovskii functional the scaling gain can be adjusted to render the closed-loop system globally asymptotically stable.The results can also be extended to the non-triangular nonlinear time-delay systems. The proposed control law together with the observer is linear and memoryless in nature and therefore it is easy to implement in practice. Two computer simulations are conducted to illustrate the effectiveness of the proposed theoretical results.

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.

Global stabilization of nonlinear systems with uncertain structure

The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function （CLF）, a sufficient and necessary condition for Lyapunov stabilization is given. From the condition, several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.

Impulsive efects on global stability of models based on impulsive diferential equations with “supremum” and variable impulsive perturbations

Sufficient conditions are investigated for the global stability of the solu tions to models based on nonlinear impulsive differential equations with ＂supremum＂ and variable impulsive perturbations. The main tools are the Lyapunov functions and Razu mikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.

Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty

This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.

STABILITY OF SOLUTIONS FOR CERTAIN THIRD-ORDER NONLINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

In this paper, we investigate stochastic asymptotic stability of the zero solution for certain third-order nonlinear stochastic delay differential equations by constructing Lyapunov functionals.

Tracking Control of Uncertain Nonlinear Systems With Unknown Constant Input Delay

A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.

TWO DIFFERENTIAL INFECTIVITY EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE

This paper considers two differential infectivity（DI） epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely., a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity,O is globally stable and the disease always dies out. If σ〉1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover,when σ〈 1 ,the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.

Global Dynamics Analysis of a Cholera Transmission Model with General Incidence and Multiple Modes of Infection

This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .

TWO TYPES OF CONDITION FOR THE GLOBAL STABILITY OF DELAYED SIS EPIDEMIC MODELS WITH NONLINEAR BIRTH RATE AND DISEASE INDUCED DEATH RATE

We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39（4） （1999） 332-352. It is assumed that the population has a nonlinear birth term and disease causes death of infective individuals. By using a monotone iterative method, we establish sufficient conditions for the global stability of an endemic equilibrium when it exists dependently on the monotone property of the birth rate function. Based on the analysis, we further study the model with two specific birth rate functions BI（N） = be-aN and B3（N） = A/N ＋ c, where N denotes the total population. For each model, we obtain the disease induced death rate which guarantees the global stability of the endemic equilibrium and this gives a positive answer for an open problem by X. Q. Zhao and X. Zou, Threshold dynamics in a delayed SIS epidemic model, J. Math. Anal. Appl. 257（2） （2001） 282-291.

STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS:A CONTROL LYAPUNOV FUNCTION APPROACH

This paper presents a control Lyapunov function approach to the global stabilizationproblem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws areproposed based on the method of control Lyapunov functions and Sontag's universal formula.

GLOBAL STABILIZATION OF LINEAR SYSTEMS WITH BOUNDED CONTROLS USING STATE-DEPENDENT SATURATION FUNCTIONS

By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach.

Global output feedback stabilization of upper-triangular nonlinear time-delay systems

In this paper, the problem of global output feedback stabilization for a class of upper-triangular nonlinear systems with time-varying time-delay in the state is considered. The uncertain nonlinearities are assumed to be higher-order in the unmeasurable states. Based on the extended homogeneous domination approach, using a low gain observer in combi- nation with controller, the delay-independent output feedback controller makes closed-loop system globally asymptotically stable under a homogeneous growth condition.

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题.首先,给出保证线性部分有一致规范型的充分条件.其次,利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定.最后,通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.

求解混合约束非线性规划的神经网络模型

通过巧妙构造Liapunov函数,提出一种大范围收敛的求解优化问题的连续神经网络模型.它具有良好的功能和性能,可以求解具有等式和不等式约束的非线性规划问题.该模型是Newton最速下降法对约束问题的推广,能有效地提高解的精度.即使对正定二次规划问题,它也比现有的模型结构简单.

若干具有非线性传染力的传染病模型的稳定性分析

讨论了具有常数迁入和非线性传染力的三类传染病模型,即SIRI 模型,SIRI 框架下的DS 模型及SIR 框架下的DI 模型.给出了它们基本再生数R_0的表达式,证明了R_0(?)1 时无病平衡点是全局稳定的,同时证明了如果地方病平衡点存在,则必是全局稳定的结果(从而必唯一).对第一和第三个模型还给出了R_0>1对地方病平衡点的存在唯一性.

不确定非线性系统变结构控制器设计

传统的控制方法大多需要知道被控对象的数学模型 ,而许多复杂的实际系统 ,其准确的数学模型往往不易得到 ,或者难以求解。采用自适应滑模变结构控制方法 ,对形如 x(n) =f( x,t) +g( x,t) u+d( t)的非线性系统进行跟踪控制 ,其中 f( x,t)和 g( x,t)为未知非线性函数 ,且其边界未知 ,d( t)为未知有界扰动 ,为减少对被控制对象信息的依赖性 ,没有利用专家知道 ,也没有利用被控对象的历史运行数据 ,通过利用基函数类神经网络动态逼近函数 f( x,t)和 g( x,t) ,对自适应调整控制系统输入 ,得出基于 RBF网络的滑模变结构自适应控制方案 ,经过理论分析 ,证明了控制方案的稳定性。

基于能量的电磁轴承系统建模及控制方法研究

通过介绍电磁轴承的基本组成,针对电磁轴承系统中的大范围稳定问题,在考虑线圈电感的非线性的情况下,从能量的角度对系统进行了非线性建模。并在构建李雅普诺夫函数及理论分析的基础上提出了基于能量的控制器方法。与传统的PID控制进行仿真对比后,得到了一组可使电磁轴承大范围稳定的参数范围。结果表明,这种方法为非线性控制提供了设计基础,在获得满意的动态响应方面是可行的。