Reduced-order filter for stochastic bilinear systems with multiplicative noise

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