RobustH2/H∞Filter Design for a Class of Nonlinear Stochastic Systems with State-Dependent Noise

Weihai Zhang,Li Sheng,Bor-Sen Chen,Ming Gao

doi:10.1155/2012/750841

Abstract

This paper investigates the problem of robust filter design for a class of nonlinear stochastic systems with state-dependent noise. The state and measurement are corrupted by stochastic uncertain exogenous disturbance and the dynamic system is modeled by Itô-type stochastic differential equations. For this class of nonlinear stochastic systems, the robustH∞filter can be designed by solving linear matrix inequalities (LMIs). Moreover, a mixedH2/H∞filtering problem is also solved by minimizing the total estimation error energy when the worst-case disturbance is considered in the design procedure. A numerical example is provided to illustrate the effectiveness of the proposed method.

Highlights

Over the past decades, the robust H∞ filtering problem has been investigated extensively since it is very useful in signal processing and engineering applications 1–5
This paper investigates the problem of robust filter design for a class of nonlinear stochastic systems with state-dependent noise
The robust H∞ filtering problem has been investigated extensively since it is very useful in signal processing and engineering applications 1–5

Summary

Introduction

The robust H∞ filtering problem has been investigated extensively since it is very useful in signal processing and engineering applications 1–5. The so-called H∞ filtering problem is to design an estimator to estimate the unknown state combination via measurement output, which guarantees the L2 gain from the external disturbance to the estimation error to be less than a prescribed level γ > 0. The robust H2/H∞ filtering problem for linear perturbed systems with steady-state error variance constraints was investigated in 6 , and the mixed H2/H∞ filter for polytopic discrete-time systems was discussed in 7. Wang et al studied the robust H∞ filtering problem for a class of uncertain time-delay stochastic systems with sectorbounded nonlinearities. There is little work dealing with the H2/H∞ filtering problem for nonlinear stochastic systems. We will deal with the robust filtering problem for a class of nonlinear stochastic systems. V t, x twice continuously differential with respect to x ∈ U and once continuously differential with respect to t > 0 except possibly at the point x 0

Problem Setting

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Numerical Example

Conclusions