On the stability of a reduced-order filter based on dominant singular value decomposition of the system dynamics

The stability of a reduced-order filter (ROF), the gain of which is constructed on the basis of a subspace of dominant singular vectors of the system dynamics, is examined. A definition of s-detectability is introduced. It is found that the observability of all unstable and neutral singular vectors (s-detectability) is a sufficient condition for the existence of a stable filter.