Abstract
The paper presents an H infinite-type filtering problem for stochastic systems subject to statedependent
(multiplicative) noise. Necessary and sufficient conditions for the existence of a fixed
(reduced) order filter are derived both for continuous-time and for the discrete-time cases. These
conditions depend on the solutions of some specific systems of linear matrix inequalities subject to a rank
minimization condition. For the considered problem it is shown that the rank constraint can be solved as a
semi-definite programming problem using a particular affine transformation.
