functional filtering for stochastic bilinear systems with multiplicative noises

This paper deals with the design of a reduced-order H ∞ filter for a stochastic bilinear system with a prescribed H ∞ norm criterion. The considered system is bilinear in control and with multiplicative noises in the dynamics and in the measurement equations. The problem is transformed into the search of a unique gain matrix by using Sylvester-like constraints. The approach is based on the resolution of LMI and is then easily implementable.