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The finite-time stability and stabilization problems of a class of networked control systems (NCSs) with bounded Markovian packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time stability and stabilization via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump linear systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time stability and stabilization of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

The concept of Lyapunov asymptotic stability is largely known to the control community; see [

On the other hand, NCSs are feedback control systems with control loops closed via digital communication channels. Compared with the traditional point-to-point wiring, the use of the communication channels can reduce the costs of cables and power, simplify the installation and maintenance of the whole system, and increase the reliability. Because of these attractive benefits, many industrial companies and institutes have shown interest in applying networks for remote industrial control purposes and factory automation [

So far, Lyapunov stability analysis for NCSs with packet dropout has been extensively studied by many researchers [

This paper is organized as follows. An iterative method to model NCSs with bounded Markovian packet dropout as MJLSs is proposed in Section

The framework of NCSs considered in this paper is depicted in Figure

Illustration of NCSs over communication network.

Let

It is worth pointing out that the packet dropout process

The main aim of this paper is to find some sufficient conditions which guarantee that the system given (

System (

To this end, the following lemmas will be essential for the proofs in the next section and theirs proofs can be found in the cited reference.

For any matrices

For a given symmetric matrix

In this section, we will find a state feedback control matrix

For a constant

Choose the Lyapunov function as

Now we turn back to our original problem, which is to find sufficient conditions which guarantee that the system (

For a constant

By Lemma

For the case of

In this section, a numerical example is given to illustrate the effectiveness of the proposed methods. Let us consider the continuous time system [

State response.

In this paper, we have considered the finite-time stabilization problems of a class of networked control systems (NCSs) with bounded Markovian packet dropout, based on the iterative approach the NCSs with bounded packet dropout as jump linear systems. The sufficient conditions for finite-time stabilization of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

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

This work was partly supported by the University Natural Science Foundation of Anhui Province no. KJ2013A239 and the University Special Foundation for Young Scientists of Anhui Province no. 2013SQRW052ZD.