Reduced order unbiased filtering for a class of uncertain bilinear systems

This paper presents a simple solution to the ℋ_∞ unbiased functional reduced order filtering problem via linear matrix inequality (LMI) methods for bilinear systems. We extend the result to the robust filtering for bilinear systems subject to structured norm-bounded time-varying uncertainties. After giving conditions for the existence of the unbiased filter in the nominal case, we show that the filter design is reduced to a small gain problem in the nominal case and to a static output feedback one when the nominal bilinear system is affected by the uncertainties