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.