Impulsive Stabilization Research Articles

New Criteria on Impulsive Stabilization and Synchronization of Delayed Unified Chaotic Systems with Uncertainty

This paper investigates stability and synchronization problems for delayed unified chaotic system with parameter uncertainty by employing the Lyapunov function method and matrix inequality techniques. Sufficient conditions for their asymptotical stability and synchronization are developed under given impulsive controllers. Finally, the validity of the obtained results is shown by a numerical example and its simulation.

Research on impulsive synchronization approach ofparameter uncertain hyperchaotic systems with time-delay

In this paper, based on the Lyapunov stability theory, the impulsive synchronization asymptotic stability condition for different hyperchaotic systems with time delay and parameter uncertainty is first presented by using the linear feedback of state variable error between the slave system and the master system as the impulsive control signal. After the synchronization, a digital communication system with time delay is provided to achieve secure communication. This scheme is of high security and robustness. Moreover, computer simulations show that in the communication system, the synchronization of the systems could be achieved quickly, and by using chaotic cipher sequence to encrypt the digital signal, the useful information signal can be recovered effectively from the receiver.

Stability in impulsive systems with Markov perturbations in averaging scheme. 2. Averaging principle for impulsive Markov systems and stability analysis based on averaged equations

The Bogoliubov---Mitropolsky small parameter method is used to study the behavior of stochastic differential systems in the analysis of the corresponding properties of solutions of averaged systems.

Impulsive Stabilization of Discrete-time Pure-delayed Neural Networks

Article Impulsive Stabilization of Discrete-time Pure-delayed Neural Networks was published on December 1, 2010 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 11, issue Supplement).

Impulsive stabilization of stochastic functional differential equations

This paper investigates impulsive stabilization of stochastic delay differential equations. Both moment and almost sure exponential stability criteria are established using the Lyapunov–Razumikhin method. It is shown that an unstable stochastic delay system can be successfully stabilized by impulses. The results can be easily applied to stochastic systems with arbitrarily large delays. An example with its numerical simulation is presented to illustrate the main results.

A New Approach for Impulsive Stabilization of Liu's System

An impulsive control scheme of Liu's system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global exponential stability for the impulsive control of Liu's systems. We also present the estimate of the stable region for the equidistance impulsive interval. Furthermore, an illustrative example is given to show the effectiveness of the proposed results.

Fuzzy Modeling and Impulsive Control of a Memristor-Based Chaotic System

We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi–Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristor-based chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.

Impulsive Stabilization of Delayed Cellular Neural Networks via Partial States

The problem of impulsive stabilization of delayed cellular neural networks (DCNNs) via partial states is discussed. The time delay is allowed to be time-varying. By utilizing the piecewise linear property of the activation function of DCNNs and applying piecewise differential Lyapunov combined with Razumikhin-type analysis techniques, a sufficient condition for the existence of the impulsive control law via partial states is derived. The sufficient condition is given in terms of linear matrix inequalities concerning the interconnection matrices and the bounds of the impulsive intervals. By using this result, an impulsive stabilization scheme for a class of DCNNs is proposed. The impulsive stabilization scheme only utilizes the output of partial states of the controlled DCNN. A numerical example illustrates the efficiency of the proposed method.

Optimal Control of Linear Impulsive Antiperiodic Boundary Value Problem on Infinite Dimensional Spaces

A class of optimal control problems for infinite dimensional impulsive antiperiodic boundary value problem is considered. Using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of the semigroup governed by original principle operator, we present the existence of optimal controls. At last, an example is given for demonstration.

Adaptive-impulsive control for projective synchronization in the drive-response complex network with time-varying coupling

Recently,most of works had studied the impulsive stabilization of networks with time-varying delays. But there are few results about synchronization criterion of networks with time-varying delays via adaptive-impulsive control. In this paper,by adaptive-impulsive control method,projective synchronization in the drive-response complex network of partially linear systems with time-varying coupling is investigated. An adaptive-feedback controller,updating laws and a linear impulsive controller are proposed. An adaptive-impulsive projective synchronization criterion of network with time-varying coupling is established. And the coupling configuration matrix in network is not required irreducible. Moreover,numerical simulation is used to verify the effectiveness of the scheme.

Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors

The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Based on the impulsive stability theory, nonlinear observer-based impulsive synchronization scheme is derived. A new and less conservative criteria for impulsive synchronization via nonlinear observer is proposed. The boundary of the stable regions is also estimated. One important advantage of the proposed method is that it is also applicable for the systems with more than one attractor. Numerical simulations on Newton–Leipnik system are illustrated to verify the theoretical results.

Impulsive stabilization of mechanical systems in Takagi–Sugeno models

Takagi-Sugeno fuzzy impulsive systems are analyzed for Lyapunov stability. Lyapunov’s second method is used to establish sufficient stability conditions for such systems. It is shown that these conditions are expressed by a system of matrix inequalities. Impulsive fuzzy control of two coupled pendulums is considered as an example

Exponential Stability of Impulsive Delayed Linear Differential Equations

This brief considers the global exponential stability of impulsive delayed linear differential equations. By utilizing the Lyapunov function methods combined with the Razumikhin technique, several criteria on exponential stability are analytically derived, which are substantially an extension and a generalization of the corresponding results in recent literature. Compared with some existing works, a distinctive feature of this brief is to address exponential stability problems for any fixed-time delays. It is shown that the delayed linear differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. An example and its simulation are also given to illustrate the theoretic results.

Uncertain impulsive differential-difference equations and stability of moving invariant manifolds

In this article we present the results of investigation on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The obtained results are based on the method of piecewise continuous Lyapunov functions and comparison principle.

Impulsive stabilization of second-order nonlinear delay differential systems

Modeling of many dynamic systems results in second-order delay differential systems. In this paper, we prove that two kinds of delay systems without impulses can be stabilized by proper impulsive control, respectively. Our results have improved and generated some of the known results found in the literature. We also give an example to illustrate the obtained results.

Impulsive Exponential Stabilization of Functional Differential Systems with Infinite Delay

By using the Razumikhin technique and Lyapunov functions, we investigated the impulsive exponential stabilization of functional differential systems with infinite delay. A new result on the exponential stabilization by impulses is gained. Our result shows that impulses can make unstable systems stable. A numerical example is given to illustrate the feasibility of the result.

Impulsive Stabilization for a Class of Neural Networks with Both Time-Varying and Distributed Delays

The impulsive control method is developed to stabilize a class of neural networks with both time-varying and distributed delays. Some exponential stability criteria are obtained by using Lyapunov functionals, stability theory, and control by impulses. A numerical example is also provided to show the effectiveness and feasibility of the impulsive control method.

Impulsive control and synchronization of chaotic Hindmarsh–Rose models for neuronal activity

The issues of impulsive control and synchronization of chaotic Hindmarsh–Rose model are investigated in this paper. Based on impulsive control theory of dynamical systems, some simple yet less conservative criteria ensuring impulsive stabilization and synchronization of the Hindmarsh–Rose models are derived analytically. Furthermore, two numerical results are presented to demonstrate the effectiveness of the proposed control techniques. It is shown that the obtained results should be helpful to understand dynamical mechanism of signal encoding and transduction from information processing of real neuronal activity.

Impulsive stability of chaotic systems represented by T-S model

In this paper, a novel and unified control approach that combines intelligent fuzzy logic methodology with impulsive control is developed for controlling a class of chaotic systems. We first introduce impulses into each subsystem of T-S fuzzy IF-THEN rules and then present a unified T-S impulsive fuzzy model for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by Lyapunov method techniques and a design procedure for estimating bounds on control matrices is also given. These results are shown to be less conservative than those existing ones in the literature and several numerical examples are presented to illustrate the effectiveness of this method.

Projective Synchronization in Drive–Response Networks via Impulsive Control

Impulsive projective synchronization in 1 + N coupled chaotic systems are investigated with the drive–response dynamical network (DRDN) model. Based on impulsive stability theory, some simple but less conservative criteria are achieved for projective synchronization in DRDNs. Furthermore, impulsive pinning scheme is also adopted to direct the scaling factor onto the desired value. Numerical simulations on generalized chaotic unified system are illustrated to verify the theoretical results.