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This paper studies the robust _{∞} filtering problem of nonlinear stochastic systems
with time delay appearing in state equation, measurement, and controlled output, where the
state is governed by a stochastic Itô-type equation. Based on a nonlinear stochastic bounded
real lemma and an exponential estimate formula, an exponential (asymptotic) mean square _{∞}
filtering design of nonlinear stochastic time-delay systems is presented via solving a Hamilton-Jacobi inequality. As one corollary, for linear stochastic time-delay systems, a Luenberger-type filter is obtained by solving a linear matrix inequality. Two simulation examples are finally given
to show the effectiveness of our results.

Robust

It is well known that time delay phenomena are often encountered in many engineering applications such as network control and communication, and a study of time delay systems has been a popular research topic for a long time [

To our best knowledge, few works on

For convenience, we adopt the following traditional notations:

Consider the following nonlinear stochastic time delay system:

Since this paper deals with the infinite horizon stochastic

The nonlinear stochastic time delayed system

Associated with (

The following lemma is a generalized version of Proposition 1 in [

Consider the following input-output system:

See Appendix

Consider the unforced system

then

See Appendix

In what follows, we construct the following filtering equation for the estimation of

Find the matrices

the equilibrium point

for a given disturbance attenuation level

If in (i) of Definition

Our first main result is about exponential mean square

Suppose that there exists a positive Lyapunov function

In Lemma

Next, we show the augmented system (

Inequality (

The following theorem is about asymptotic mean square

Assume that

Obviously, it only needs to show that (

By Itô’s formula and the property of stochastic integration, we have

As one application of Theorem

If (

Below, we give two examples to illustrate the validity of our developed theory in the above section.

Suppose that a stochastic signal

Simulation results for Example

The trajectories of

The trajectories of

In (

Simulation results for Example

The trajectories of

The trajectories of

This paper presents an approach to the design of

As done in [

By (

This work was supported by the National Natural Science Foundation of China (60874032, 60804034, 61174078), Specialized Research Fund for the Doctoral Program of Higher Education (20103718110006) and Key Project of Natural Science Foundation of Shandong Province (ZR2009GZ001).

_{∞}filtering of stationary continuous-time linear systems with stochastic uncertainties

_{∞}optimal linear filtering problem for discrete-time systems

_{∞}filtering for nonlinear systems

_{∞}filtering for uncertain stochastic time-delay systems

_{∞}filtering algorithm

_{∞}filtering for nonlinear stochastic systems

_{∞}control for a class of nonlinear stochastic systems

_{∞}filtering on nonlinear stochastic systems with delay

_{∞}analysis of nonlinear stochastic time-delay systems