Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.     

Stability Analysis and Design of Impulsive Control Lorenz Systems Family

Lorenz systems family unifying Lorenz system, Chen system and Lü system is a typical chaotic family. In this paper, we consider impulsive control Lorenz chaotic systems family with time-varying impulse intervals. By establishing an effective tool of a set of inequalities, we analyze the asymptotic stability of impulsive control Lorenz systems family and obtain some new less conservative conditions. Based on the stability analysis, we design a novel impulsive controller with time-varying impulse intervals. Illustrative examples are provided to show the feasibility and effectiveness of our method. The obtained results not only can be used to design impulsive control for Lorenz systems family, but also can be extended to other chaotic systems.     

Stability Analysis for Systems with Impulse Effects

In the present paper the authors establish new conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulsive effects described by systems of nonlinear, time-varying ordinary differential equations. For the case when the corresponding systems without impulsive effects admit unstable properties, the above results are used to establish conditions under which the uniform stability even uniform asymptotic stability of equilibria of systems with impulsive effects can be caused by impulsive perturbations . 1991 Mathematics Subject Classification. 34D 20, 34K 20.     

Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Cooperative impulsive formation control for networked uncertain Euler–Lagrange systems with communication delays

This paper investigates the cooperative formation problem via impulsive control for a class of networked Euler–Lagrange systems. To reduce the energy consumption and communication frequency, the impulsive control method and cooperative formation control approach are combined. With the consideration of system uncertainties and communication delays among agents, neural networks-based adaptive technique is used for the controller design. Firstly, under the constraint that each agent interacts with its neighbors only at some sampling moments, an adaptive neural-networks impulsive formation control algorithm is proposed for the networked uncertain Euler–Lagrange systems without communication delays. Using Lyapunov stability theory and Laplacian potential function in the graph theory, we conclude that the formation can be achieved by properly choosing the constant control gains. Further, when considering communication delays,a modified impulsive formation control algorithm is proposed, in which the extended Halanay differential inequality is used to analyze the stability of the impulsive delayed dynamical systems. Finally, numerical examples and performance comparisons with continuous algorithm are provided to illustrate the effectiveness of the proposed methods.     

Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization

This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results.     

Impulsive control of chaotic systems and its applications in synchronization

In this paper,some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems.The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control.Compared with some existing results,our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings.Moreover,a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.     

基于自适应-脉冲控制方法实现时变耦合驱动-响应复杂网络的投影同步

最近,对时变延迟网络的脉冲稳定性的研究大量出现,但通过自适应-脉冲控制方法获得的时变延迟网络同步准则却很少.本文中,运用自适应-脉冲控制方法,设计自适应反馈控制器、自适应律和线性脉冲控制器,研究时变耦合部分线性系统驱动-响应复杂网络的投影同步.获得时变耦合网络的自适应-脉冲投影同步准则.并且不需要网络的耦合构造矩阵是不可约的.另外,运用数值模拟证实方案的有效性和可行性.     

Integral sliding mode control for a class of nonlinear neutral systems with time-varying delays

This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feas.ibility of the proposed technique.     

Impulsive Synchronization of Laser Plasma System

The issue of impulsive synchronization of the coupled chaotic laser plasma system is investigated. A new framework for impulsive synchronization of such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. We derive some sufficient conditions for the synchronization of a laser plasma system via impulsive control with the varying impulsive intervals, which allows us to derive the impulsive synchronization law easily. To illustrate the effectiveness of the proposed results, two numerical examples are given.     

Approximate controllability of nonlinear impulsive differential systems

Many practical systems in physical and biological sciences have impulsive dynamical be- haviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability issue for nonlinear impulsive differential and neutral functional differential equations in Hilbert spaces. Based on the semigroup theory and fixed point approach, sufficient conditions for approximate controllability of impulsive differential and neutral functional differential equations are established. Finally, two examples are presented to illustrate the utility of the proposed result. The results improve some recent results.     

基于改进脉冲控制方法的超混沌系统同步

针对一类整数阶与分数阶超混沌系统的同步问题, 分别提出了改进的脉冲同步方法. 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出超混沌系统一组新的全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更次保守且更为实用. 通过对超混沌Chen系统同步的数值仿真研究, 验证了所提方法的有效性和可行性.     

Stability analysis of nonlinear stochastic differential delay systems under impulsive control

In this Letter, we study the stability of nonlinear stochastic differential delay systems under impulsive control. First, we construct an impulsive control for a nonlinear stochastic differential delay system. Then, the equivalent relation between the stability of the nonlinear stochastic differential delay system under impulsive control and that of a corresponding nonlinear stochastic differential delay system without impulses is established. Third, some sufficient conditions ensuring various stabilities of the nonlinear stochastic differential delay systems under impulsive control are obtained. Finally, an example is also discussed to illustrate the effectiveness of the obtained results.     

基于比较系统方法的分数阶混沌系统脉冲同步控制

针对一类分数阶混沌系统的同步问题, 提出基于比较系统理论的脉冲同步方法. 通过构造新的响应系统, 可将原分数阶同步误差系统转化为整数阶同步误差系统, 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出一组新的分数阶混沌系统全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更为严格和实用. 通过对分数阶Chen系统同步问题的数值仿真研究, 验证了所提方法的有效性和可行性.     

Impulsive control for synchronization of nonlinear Rossler chaotic systems

This paper reports that an impulsive control theory for synchronization of nonlinear R?ssler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear R?ssler chaotic systems and the simulation results demonstrate the effectiveness of the method.     

Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays

In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen-Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.     

忆阻混沌系统的脉冲同步与初值影响研究

以光滑三次型磁控忆阻器的蔡氏电路为例, 研究了两个同构忆阻混沌系统的脉冲控制同步方法.基于Lyapunov稳定性理论, 给出了忆阻混沌系统的脉冲同步渐近稳定条件; 结合误差系统的最大条件Lyapunov指数谱, 讨论了系统初值对脉冲同步性能的影响, 并进行了相应的数值仿真实验.结果表明, 在合适的脉冲控制参数条件下, 同构的忆阻混沌系统的脉冲同步是可行而有效的; 忆阻混沌系统的初值对脉冲同步性能存在一定的影响, 但可通过增大脉冲耦合强度来抑制系统初值的影响.     

Modified impulsive synchronization of fractional order hyperchaotic systems

In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.     

Fuzzy modeling and impulsive control of hyperchaotic Lü system

This paper presents a novel approach to hyperchaos control of hyperchaotic systems based on impulsive control and the Takagi--Sugeno (T--S) fuzzy model. In this study, the hyperchaotic Lü system is exactly represented by the T--S fuzzy model and an impulsive control framework is proposed for stabilizing the hyperchaotic Lü system, which is also suitable for classes of T--S fuzzy hyperchaotic systems, such as the hyperchaotic R?ssler, Chen, Chua systems and so on. Sufficient conditions for achieving stability in impulsive T--S fuzzy hyperchaotic systems are derived by using Lyapunov stability theory in the form of the linear matrix inequality, and are less conservative in comparison with existing results. Numerical simulations are given to demonstrate the effectiveness of the proposed method.     

一个新混沌系统的脉冲控制与同步

考虑黄玮提出的新混沌系统,给出了该系统的脉冲控制与同步的充分条件, 并通过仿真实验验证了所给充分条件的正确性.在所给的充分条件中,所选取的矩阵B不必是对称矩阵,因此所给条件有更大的实用性.