^{1}

^{2}

^{1}

^{2}

The problem of robust

Stochastic pantograph system which is treated as a special class of time-delay systems has also attracted more and more researchers [

On the other hand, due to great many applications of robust

In this paper, we first consider the problem on the asymptotic mean-square stability and give a test criterion for stochastic pantograph systems by the Lyapunov approach. On this basis, a sufficient condition of the asymptotic mean square stability is obtained, which can be available for studying the

This paper is organized as follows. Section

Consider the following linear stochastic pantograph system:

The stochastic pantograph system (

Stochastic pantograph system (

Expressing the difference

On the basis of Lemma

If the following linear matrix inequality

Take a Lyapunov function

Inequality (

When

Let

Based on the asymptotic mean-square stability of pantograph system discussed in the above section, we are in a position to deal with the

Consider the following stochastic linear perturbed pantograph system with measurement output:

The so-called

In what follows, we will give the main result of

If the following matrix inequality

When

Next, we prove

If

Let

It is difficult to solve the inequality (

If the following LMI

By Schur Complement, (

Taking

Setting

In the proof of Theorem

In many engineering applications, the performance constraint is often specified a priori. In Theorem

The optimal

Then the minimum value of optimal

The minimum value of

Consider the following steps.

The smallest

In this section, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed methods. Consider the following Itô stochastic pantograph system:

Consider the following filter for estimation of

The initial condition in the simulation is assumed to be

The trajectories of

The trajectories of

The trajectories of

The trajectories of

By the OP2, the minimum value of

The minimum value of

The minimum value of

This paper has discussed infinite horizon

The

The set of all

Identify matrix

The mathematical expectation operator

The space of nonanticipative square integrable stochastic processes

The family of all nonnegative functions

This work is supported by the Starting Research Foundation of Shandong Polytechnic University under Grant 12045501, Outstanding Mid-Young Scientist Prize Foundation of Shandong Province (BS2011DX032), and a Project of Shandong Province Higher Educational Science and Technology Program (J10LG13).