Lur''''e系统稳定与同步的脉冲控制

提出了Lur’e系统的脉冲控制系统，利用关于脉冲系统稳定的几个定理，得到了具变化的脉冲区间的Lur'e系统镇定的充分条件；并且给出了Lur'e系统的适当参数与脉冲控制律，使得两个Lur'e系统脉冲同步。最后，给出数值例子说明本结论的有效性。     

Variable impulsive consensus of nonlinear multi-agent systems

In this paper, the consensus problem for nonlinear multi-agent systems with variable impulsive control method is studied. In order to decrease the communication wastage, a novel distributed impulsive protocol is designed to achieve consensus. Compared with the common impulsive consensus method with fixed impulsive instants, the variable impulsive consensus method proposed in this paper is more flexible and reliable in practical application. Based on Lyapunov stability theory and some inequality techniques, several novel impulsive consensus conditions are obtained to realize the consensus of multi-agent systems. Finally, some necessary simulations are performed to validate the effectiveness of theoretical results.     

Oscillation and other properties of linear impulsive and nonimpulsive delay equations

Many of the oscillation results for linear impulsive equations were justified by the following scheme. First, the equivalence of the oscillation of the impulsive equation and some specially constructed nonimpulsive equation was established; further, on the base of well-known results for the nonimpulsive case, the oscillation of the impulsive equation was analyzed. In the present paper, we prove the “oscillation equivalence” result for a linear impulsive equation with a distributed delay and discuss the possibility to expand this approach to the other properties of impulsive equations, for example, stability and asymptotic behavior. In addition, a linear impulsive equation of the second order is considered.     

T-S模糊系统的脉冲稳定性

针对模糊控制系统提出了一种新的稳定性设计方法.该方法在传统T-S模型的局部子系统中引入脉冲控制项,构造了具有脉冲影响的模糊控制系统.然后,通过去模糊化技术,把具有脉冲影响的模糊系统转化为脉冲微分系统.这样,借助脉冲微分方程的比较原理和线性矩阵不等式技术,给出了模糊系统的脉冲稳定的充分条件.从而建立了模糊系统的简单脉冲控制策略.     

On impulsive control for synchronization and its application to the nuclear spin generator system

The issue of impulsive control theory for the synchronization of the nuclear spin generator (NSG) chaotic systems is developed. We propose an impulsive control scheme for the complete synchronization of the NSG system including chaotic systems. A sufficient condition for the impulsive control is derived, with an easily calculated maximum impulsive interval. The proposed impulsive control scheme is applied to the NSG system and the simulation result demonstrates the effectiveness of the method.     

Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control

This paper is concerned with the global exponential synchronization problem of two identical nonlinear time-delay Lur’e systems via delayed impulsive control. Some novel impulsive synchronization criteria are obtained by introducing a discontinuous Lyapunov function and by using the Lyapunov–Razumikhin technique, which are expressed in forms of linear matrix inequalities. The derived criteria reveal the effects of impulsive input delays and impulsive intervals on the stability of synchronization error systems. Then, sufficient conditions on the existence of a delayed impulsive controller are derived by employing these newly-obtained synchronization criteria. Additionally, some synchronization criteria for two identical time-delay Lur’e systems with impulsive effects are presented by using delayed continuous feedback control. The synchronization criteria via delayed continuous feedback control can deal with the case when the impulsive control strategy fails to synchronize two identical impulsive time-delay Lur’e systems. Three numerical examples are provided to illustrate the efficiency of the obtained results.     

Topological conjugation and asymptotic stability in impulsive semidynamical systems

We prove several results concerning topological conjugation of two impulsive semidynamical systems. In particular, we prove that the homeomorphism which defines the topological conjugation takes impulsive points to impulsive points; it also preserves limit sets, prolongational limit sets and properties as the minimality of positive impulsive orbits as well as stability and invariance with respect to the impulsive system. We also present the concepts of attraction and asymptotic stability in this setting and prove some related results.     

Network synchronization under distributed delayed impulsive control: Average delayed impulsive weight approach

This paper mainly investigates synchronization of complex dynamical networks (CDNs) with both system delay and coupled delay through distributed delayed impulsive control. Instead of constraining the impulsive weight and impulsive delay one by one, a new concept of average delayed impulsive weight is proposed to obtain more relaxed conditions. Subsequently, based on the impulsive control topology, Lyapunov theory and linear matrix inequality (LMI) design, certain flexible criteria of global exponential synchronization (GES) are given and the corresponding convergence rate is estimated. It is interesting to see that the CDNs can still achieve synchronization under comprehensive conditions though impulsive weights work negatively. Namely, the delays in impulsive control are able to promote synchronization potentially. Finally, simulations are given to show that the distributed delayed impulsive control can not only speeds up the convergence rate for synchronized networks, but also facilitates synchronization for desynchronized networks. In addition, the obtained results can be applied to unmanned craft systems.     

Existence and exponential stability of periodic solution for impulsive delay differential equations and applications

In this paper, we consider a class of nonlinear impulsive delay differential equations. By establishing an exponential estimate for delay differential inequality with impulsive initial condition and employing Banach fixed point theorem, we obtain several sufficient conditions ensuring the existence, uniqueness and global exponential stability of a periodic solution for nonlinear impulsive delay differential equations. Furthermore, the criteria are applied to analyze dynamical behavior of impulsive delay Hopfield neural networks and the results show different behavior of impulsive system originating from one continuous system.     

An impulsive controlled eco-epidemic model with disease in the prey

In this paper, we investigate the dynamic behavior of an eco-epidemic model with impulsive control strategy. By using Floquet theorem of impulsive differential equation, we show there is a globally stable prey eradication periodic solution when the impulsive period is less than some critical value. We study the permanence of the system. Numerical simulations show that the complex dynamics of the system depends on the values of impulsive period and impulsive perturbation, for example double period, triple period solutions.     

The effects of impulsive harvest on a predator–prey system with distributed time delay

A kind of predator–prey system with distributed time delay and impulsive harvest is firstly presented and then the effects of impulsive harvest on the system are discussed by means of chain transform. By using the Floquet’s theory and the comparison theorem of impulsive differential equation, the thresholds between permanence and extinction of each species are obtained as functions of model parameters. It is proved that the impulsive period and the proportion of the impulsive harvest will ultimately affect the fate of each species. Finally, the theoretical results obtained in this paper are confirmed by numerical simulations.     

Stability of impulsive functional differential equations via the Liapunov functional

In this work, we investigate the stability of a class of impulsive functional differential equations. Some general stability theorems are obtained. Our results can be applied to finite delay impulsive systems or infinite delay impulsive systems or impulsive systems involving both finite and infinite delays, in a unified way. Examples are also given to illustrate that applying our theorems yields better conclusions than the results in the literature.     

Discrete time adaptive impulsive control theory

This paper considers both impulsive and adaptive control of discrete time Markov processes. The first part deals with impulsive control with a long run average cost criterion. Under suitable assumptions the optimal impulsive strategies are characterized. In the second part, based on the impulsive control results obtained earlier, the optimal adaptive controller is constructed. With the use of so-called modified maximum likelihood estimation, value consistency is obtained.     

Bifurcation of a three molecular saturated reaction with impulsive input

Although impulsive differential equations have become a widely concerned subject and a lot of models with impulsive effect have been studied in recent years, biochemical reaction models with impulsive input are rarely studied. In this paper, we consider an irreversible three molecular reaction model with impulsive input. By using the Floquet theorem and the method for the small parameter of impulsive differential equations, we obtain sufficient conditions for asymptotical stability and global stability of the given system. The existence of a positive periodic solution is also studied by the bifurcation theory. Further, we also show that our given conditions are right by numerical simulations.     

Optimal control of impulsive Volterra equations with variable impulse times

We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive Volterra control with fixed impulse times.     

Impulsive synchronization of time-varying dynamical network

Synchronization of time-varying dynamical network is investigated via impulsive control. Based on the Lyapunov function method and stability theory of impulsive differential equation, a synchronization criterion with respect to the system parameters and the impulsive gains and intervals is analytically derived. Further, an adaptive strategy is introduced for designing unified impulsive controllers, with a corresponding synchronization criterion derived. In this proposed adaptive control scheme, the impulsive instants adjust themselves to the needed values as time goes on, and an algorithm for determining the impulsive instants is provided and evaluated. The derived theoretical results are illustrated to be effective by several numerical examples.     

线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

Impulsive non‐autonomous dynamical systems and impulsive cocycle attractors

In this work, we define the notions of ‘impulsive non‐autonomous dynamical systems’ and ‘impulsive cocycle attractors’. Such notions generalize (we will see that not in the most direct way) the notions of autonomous dynamical systems and impulsive global attractors in the current published literature. We also establish conditions to ensure the existence of an impulsive cocycle attractor for a given impulsive non‐autonomous dynamical system, which are analogous to the continuous case. Moreover, we prove the existence of such attractor for a non‐autonomous 2D Navier–Stokes equation with impulses, using energy estimates. Copyright © 2016 John Wiley & Sons, Ltd.