Reduced ℋ2 and ℋ∞ observers-singular measurement noise case

In the present paper, both ℋ₂ and ℋ_∞ singular estimation problems are solved in a new way. The results are obtained by continuity with the regular case. It is shown that, when the singular case is approached, the Riccati equation can be shared in 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 becomes 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