Optimal filtering for multirate systems

For a multirate system where the output sampling is slower than the input updating, this brief aims at designing filters for fast state estimation in the H₂ and H_∞ settings. Because of the multirate nature, linear matrix inequality solutions to the design problems involve a nonconvex constraint, which is numerically tackled by the product reduction algorithm. Finally, a design example is given and the effectiveness of the approach is illustrated.