Quasi-unknown input observers for linear systems

Unknown input observers (UIO) are well-known in the literature for linear systems, in particular in the fault detection and identification area. Their particularity rests in the possibility of obtaining an exact asymptotic estimation of the state or a functional of it despite of completely unknown input disturbances. However, conditions for this to be possible are very restrictive, what reduces considerably the applicability and usefulness of UIOs. In the paper a method to reduce the severity of such conditions is proposed. The cause for the highly restrictive conditions for UIOs lies in the fact that the unknown input is assumed to be completely arbitrary, i.e. no knowledge about it is assumed. However, in practice some information about them is available, and one could use it to design an observer that is robust to such kinds of inputs. We propose the use of a linear model of the unknown inputs and an observer robust to such kinds of inputs is designed. This reduces the necessary conditions for its existence. It is intuitively clear that the more information on the disturbances is known the less restrictive the conditions for the existence of a robust observer are, as is shown in the paper.