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The problem of network-based robust filtering for stochastic systems with sensor nonlinearity is investigated in this paper. In the network environment, the effects of the sensor saturation, output quantization, and network-induced delay are taken into simultaneous consideration, and the output measurements received in the filter side are incomplete. The random delays are modeled as a linear function of the stochastic variable described by a Bernoulli random binary distribution. The derived criteria for performance analysis of the filtering-error system and filter design are proposed which can be solved by using convex optimization method. Numerical examples show the effectiveness of the design method.

In recent years, networked control systems (NCSs) have been extensively investigated due to thier broad applications in industrial engineering [

Stochastic phenomenon frequently exhibits in many branches of science and engineering applications [

In practical physical systems, sensors and actuators cannot always provide unlimited amplitude signal mainly due to the physical or safety constraints [

It should be pointed out that, if we consider the filtering problem for stochastic systems in a realistic networked environment, the effects of sensor saturation, sensor quantization, and random communication delay always exhibit simultaneously. However, in networked environments, the sensor saturation may occur to be involved with state-dependent disturbance, and it may result from random sensor failures leading to intermittent saturation, sensor aging resulting in changeable saturation level, repairs of partial components, changes in the interconnections of subsystems, and so forth. Therefore, when investigating the filtering problems of NCSs with a stochastic plant, the model under consideration should be more comprehensive to reflect the realities such as the the state-dependent stochastic disturbances, the coupling effects of sensor saturation, output quantization, and networked-induced transmission delay. Unfortunately, however, to the best of the authors’ knowledge, the

In this paper, we are concerned with the filter design problem for discrete-time networked stochastic systems subject to output saturation, quantization, and random communication delay. The networked-induced communication delay phenomena are modeled by a Bernoulli random binary distributed white sequence with a known conditional probability. In this network setting, the effects of sensor saturation, output quantization, and communication delay in the digital communication channel exhibit simultaneously, and the signal received in the filter side is imperfect. The objective is to analyze and design a robust filter such that the asymptotic estimates of system states are obtained by employing the incomplete output measurements. Moreover, sufficient conditions will be proposed such that the derived filtering error system is robustly stochastically stable with a prescribed disturbance attenuation level. Finally, a numerical example is provided to illustrate the effectiveness of the proposed filtering design approach.

Throughout the paper,

We consider the following discrete-time stochastic system with state-dependent disturbance:

In plant (

Besides, it is assumed that the exogenous disturbance

As seen in plant (

The structure of the quantized filtering system is illustrated in Figure

The structure of networked filtering systems.

We denote

In this paper, we employ the

In fact, the logarithmic quantizer (

In this filtering problem, the measured output received in the

For simplicity, we denote

We define the following error variables:

System (

Before formulating the problem to be investigated, we introduce the following definition and lemma.

The stochastic system (

For any real vectors

In the sequel, the main objective of this paper is as follows.

In this section, we shall focus on the

If there exist positive and definite matrices

Consider the filtering error system (

In the light of (

(i) Firstly, we establish the stochastic stability of the filtering error system (

It is obvious that if

(ii) Next, the objective should be devoted to prove that the filtering error system (

In fact, under zero initial conditions, it is shown that

It follows from (

In this section, the attention should be paid on coping with the addressed filter design problem for the discrete-time stochastic system (

Let

The following theorem provides the sufficient LMI condition for the existence of the proposed robust filter (

Consider the discrete-time stochastic system (

then the

The matrix condition (

The LMI condition (

We consider the system (

Besides, the model parameters are given as follows:

In this paper, the

This work is supported by the National High Technology Research and Development Program of China (no. 2012AA120601), National Natural Science Foundation of China (no. 11202044 and no. 11072044) and the Fundamental Research Funds for the Central Universities.