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The problem of impulsive control for memristor-based chaotic circuit systems with impulsive time windows is investigated. Based on comparison principle, several novel criteria which guarantee the asymptotic stabilization of the memristor-based chaotic circuit systems are obtained. In comparison with previous results, the present results are easily verified. Numerical simulations are given to further illustrate the effectiveness of the theoretical results.

In 1971 [

We also note that impulsive control has been widely used to stabilize and synchronize chaotic systems [

In this paper, we are concerned with the asymptotical stabilization problem for a class of memristive chaotic systems with impulsive time window. Based on comparison principle, we will propose several novel criteria for the stabilization of memristive chaotic system with impulsive time window. The main contributions of this paper can be highlighted as follows: (1) a new memristive chaotic system model is established to consider impulsive time window, where impulsive effects can exist at a random moment of a determined time interval; (2) by using comparison principle, sufficient criteria are derived to ensure that memristive chaotic system with impulsive time window is asymptotically stable; (3) an impulsive time window, memristive for modeling the chaotic systems simultaneously, renders more practical significance of current research.

The remainder of the paper is organized as follows. The considered model of a general memristive chaotic system with impulsive time window is presented in Section

Consider the memristor-based chaotic circuit of [

The memristor chaotic circuit [

Let

Usually, in order to obtain the chaos generation, we settled the realistic parameter values which yield chaotic dynamic as

Simulation results by MATLAB, the chaotic attractor codified by (

Similar to the method presented in [

By introducing the impulsive effects into the model [

The following definitions and lemmas are presented for the derivation of the main results.

Let

Let

Given any real matrices

Assume that

there exists a

Consider the following system:

Let

From

So

Hence

In this section, the problem of impulsive control for memristive chaotic system with impulsive time window is studied. We will find the impulsive time window

The matrix

Let the Lyapunov function be in the form of

For

Hence the second condition of Definition

Since

For

Hence condition 3 of Definition

Therefore, condition 4 of Definition

It follows from Lemma

Theorem

Let

Let the Lyapunov function be in the form of

For

Hence the second condition of Definition

Since

For

Hence the third condition of Definition

Since

It follows from Lemma

The above theorem gives an estimation of the upper boundary of

Le

If the impulse window

We consider the impulsively controlled memristor-based chaotic circuit system with impulsive time windows

In this example, we choose the matrix

We find that

Taking the initial condition

Figure

The estimation of boundaries of stable region with different

Time response curves of

In this paper, we investigated the problem of impulsive control for a class of memristive chaotic systems with impulsive time windows. The new impulsive control strategy where the impulsive effects can occur at a random moment of a determined time interval has been formulated. By using comparison principle, some sufficient conditions which ensure asymptotic stability for the model considered have been obtained. Future research topics include the extension of the results to more high-order memristive systems and delay memristive systems.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This research is supported by the Natural Science Foundation of China (Grants nos. 61302180 and 61403050) and Postdoctoral Science Foundation of China (Grant no. 2014M562266).