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This paper studies the problem of observer-based stabilization of stochastic nonlinear systems with limited communication. A communication channel exists between the output of the plant and the input of the dynamic controller, which is considered network-induced delays, data packet dropouts, and measurement quantization. A new stability criterion is derived for the stochastic nonlinear system by using the Lyapunov functional approach. Based on this, the design procedure of observer-based controller is presented, which ensures asymptotic stability in the meansquare of the closed-loop system. Finally, an illustrative example is given to illustrate the effectiveness of the proposed design techniques.

Stochastic variables frequently exist in practical systems such as aircraft systems, biology systems, and electronic circuits. Without taking them into account in the system design, the stochastic variables can bring negative effects on the performance of control systems and even make the systems unstable. According to the way stochastic variable occurs, stochastic system mode can be classified as Itô stochastic differential equation [

In the past two decades, network-based control technology has been developed to combine a communication network with conventional control systems to form the Network Control Systems (NCSs), which have wide applications due to their advantages, such as reduced weight, power requirements, low installation cost, and easy maintenance [

Among the reported results, most NCSs are mainly based on deterministic physical plant. However, stochastic systems models also have wide applications in the dynamical systems. This has motivated the researches on networked control for stochastic systems and many results have been reported in the literature. In [

In this paper, we investigate the problem of observer-based stabilization of stochastic nonlinear systems with limited communication. A new model is proposed to describe the stochastic nonlinear systems with a communication channel, which exists between the output of the stochastic plant and the input of the observer-based controller. Based on this, the design procedure of observer-based controller is proposed, which ensures the asymptotic stability of the resulting closed-loop system. Finally, a mechanical system example consisted of two cars, a spring and a damper, is given to illustrate the effectiveness of the proposed controller design method.

Consider the following stochastic nonlinear system:

For system (

Under control law (

The structure of the stochastic systems with limited communication is shown in Figure

The stochastic systems with limited communication.

In this paper, the quantizer is chosen as the logarithmic quantizer. The set of quantized levels is described by:

When taking into account signal transmission delays

A natural assumption on the network induced delays

As the time sequence

Considering the quantization shown in (

Before proceeding further, we introduce the following assumption and lemma, which will be used in subsequent developments.

For a stochastic system mode, there exists known real constant matrices

Given appropriately dimensioned matrices

In this section, the problem of asymptotical stabilization of stochastic system with limited communication is studied. We are first concerned with the asymptotical stability analysis problem. The following theorem develops a sufficient condition for system (

The nominal stochastic system (

For technical convenience, we rewrite (

Since our main objective is to design

There exists an observer-based controller such that the closed-loop system in (

Moreover, if the above conditions are satisfied, a desired controller gain and observer gain are given as follows:

Define the following matrix:

Then, by using Lemma 1 in [

In this section, we use a mechanical example to illustrate the applicability of the theoretical results developed in this paper.

The controlled plant is a mechanical system consisted of two cars, a spring, and a damper, as shown in Figure

Mechanical system.

Choose the following set of state variables:

The equations of the mechanical system are in the following:

State responses of closed-loop system.

Network-induced delays.

Data packet dropouts.

Measurements and transmitted signals.

In this paper, the problem of observer-based stabilization of the stochastic nonlinear systems with limited communication has been studied. A new model has been proposed to describe the stochastic nonlinear systems with a communication channel, which exists between the output of the physical plant and the input of the dynamic controller. Based on this, the design procedure of observer-based controller has been proposed, which guarantees the asymptotic stability of the closed-loop systems. Finally, a mechanical system example is given to show the effectiveness of the proposed controller design method.

This work was partly supported by the Postdoctoral Science Foundation of China (2011M501076), the Research Foundation of Education Bureau of Heilongjiang province (11551492), the National Key Basic Research Program of China (2012CB215202), the 111 Project (B12018), and the National Natural Science Foundation of China (61174058).

_{2}/H∞ control design of linear systems with time-varying delays: an LMI approach