Reduced order H2 and H∞ observers-singular measurement noise case

In this paper, both H₂ and H_∞ singular estimation problems are solved in a new way. The results are obtained by taking the limit from the regular case. It is shown that at the neighborhood of the singular case, the Riccati equation can be shared into two parts. The first one is a reduced Riccati equation and the second one consists of quantities tending to 0. The asymptotic gain which is then obtained tends to infinity with a special structure. Some observer modes become infinite with a finite imaginary part. Finally, the resulting observer becomes singular in singular perturbation sense. It can be calculated by solving a reduced standard problem