Contents I. Introduction
In THE PAST decade, a great amount of effort has been continuously made on filtering problem due to its major theoretical and practical significance in control engineering and signal processing. Among different filtering techniques, people are particularly interested in filter, since it has the advantages of no statistical assumptions on the exogenous noises and admitting the system model to have uncertainty. filter design approach considers the worst case from the process noise to the estimation error minimized, which is very useful in many practical applications. A number of significant results on filtering have been reported in literature. To mention a few, filtering problem has been solved for linear systems with uncertain disturbances [7], [8], hybrid systems [4], [37], singular systems [5], [13], and T-S fuzzy systems [20], [24]. However, it has been well recognized that measurement outputs of a dynamic system contain incomplete observations in practice as contingent failures are possible for all sensors in a system, see for example, [1], [17] and references therein. This phenomenon makes filter performances degrade and possible hazards happen, see for example, [19] and [32]. Therefore, the problem of reliable filter design has become an important issue and received a more attention recently. For example, reliable filtering problems have been thoroughly investigated in [24] and [38] for discrete time-delay systems. As for T-S fuzzy systems [9], [10], [33], [34], reliable filtering problems with sensor faults have also attracted many research interests [28], and [15] has considered the actuator nonlinearity and parameter uncertainties in the vehicle suspension model and constructed the T-S fuzzy model to represent the nonlinear uncertain suspension systems by using the sector nonlinearity approach.
