Robust $H_{\infty}$ Filtering for Time-Delay Systems With Probabilistic Sensor Faults

In this paper, a new robust H _infin filtering problem is investigated for a class of time-varying nonlinear system with norm-bounded parameter uncertainties, bounded state delay, sector-bounded nonlinearity and probabilistic sensor gain faults. The probabilistic sensor reductions are modeled by using a random variable that obeys a specific distribution in a known interval [alpha,beta], which accounts for the following two phenomenon: 1) signal stochastic attenuation in unreliable analog channel and 2) random sensor gain reduction in severe environment. The main task is to design a robust H _infin filter such that, for all possible uncertain measurements, system parameter uncertainties, nonlinearity as well as time-varying delays, the filtering error dynamics is asymptotically mean-square stable with a prescribed H _infin performance level. A sufficient condition for the existence of such a filter is presented in terms of the feasibility of a certain linear matrix inequality (LMI). A numerical example is introduced to illustrate the effectiveness and applicability of the proposed methodology.

I. Introduction

The state estimation problem of dynamic systems has attracted persistent research attention and has found many practical applications during the last decades. Fundamentally, two classes of performance indices have been considered in the literature based on the assumptions on the input noise [5]. In the classical filtering approach, the noise characteristics are assumed to be known, leading to the minimization of the norm of the transfer function from the process noise to the estimation error. The alternative filtering, which was first introduced in 1989 [2], has relaxed the boundedness assumption of the noise variance [12]. Over the past decades, much work has been done on the robust filtering problem in the presence of parameter uncertainties in various settings [3], [4], [18].