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Globally exponential stability of Complex (with coupling) Nonlinear Singular Impulsive Networked Control Systems (CNSINCS) with packet dropouts and time-delay is investigated. Firstly, the mathematic model of CNSINCS is established. Then, by employing the method of Lyapunov functional, exponential stability criteria are obtained and the impulsive controller design method is given. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.

At present, singular system is widely used in the control of spacecraft, flexible robot, complex power, large chemical and wireless transmission system [

On the other hand, singular system has impulsive behavior in many cases [

In network impulsive control system packet dropouts and time-delay exist which will influence the stability of singular system. It is necessary to analyze stability condition and the method of controller design. That is the problem focussed in this study. According to the Lyapunov function theory and comparison theorem, the sufficient conditions for the global exponential stability of the system is obtained. The detailed design process of impulsive controller is given in the paper. System will be stable in accordance with the decay rate to achieve exponential stability. A numerical example is provided to illustrate the correctness of theoretical and the effectiveness of design method.

The mathematic model of CNSINCS can be described as

In the process of data transmitting, the buffer’s model can be described as:

The impulsive controller can be designed as

Let

According to the definition of Kronecker product, for a given matrix

If

If

For the nonlinear singular networked impulsive control system (

If there exist

From [

When

On the other hand, when

In the following, we will prove that the following inequality holds:

which implies conclusion (

For the case

The proof of the above conclusion remains largely the same as Theorem

According to Theorem

Calculate the parameters

Choose a matrix

For a given parameter

In this section, a numerical example is presented to illustrate the effectiveness of derived results.

Consider the following complicated nonlinear singular system:

The state response of CNSINCS via impulsive control (color online).

Figure

In this paper, the global exponential stability CNSINCS via impulsive control is investigated. According to the Lyapunov stability theory, the mathematic model of CNSINCS is established. A general model of network consisting of time-delay and packet dropouts has been formulated and the globally exponential stable sufficient conditions have been established. Impulsive controller, which may ensure the system achieves exponential stability with a given decay rate is designed. Therefore our control scheme is efficient and practical in dealing with problems of data transmission with time-delay and packet dropouts. As an application, a numerical simulation is given to demonstrate the usefulness and practicability of proposed theoretical results.

This work was supported by the Jiangsu Planned Projects for Postdoctoral Research Funds under Grants 1202005C and the Jiangsu Natural Science Funds for Young Scholar under Grants BK20130696.

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