Linear system unknown input observer design when the observer matching condition is not satisfied

This paper discusses unknown input observer design method for a class of linear systems with unknown inputs when the observer matching condition (OMC) is not satisfied. Firstly, in order to break through the restriction of the OMC, a new auxiliary output construction method, which has nothing to do with the concept of relative degree with respect to the unknown input, is proposed. Then, the original system is transformed into an augmented linear descriptor system which contains no unknown inputs. In view of the transformation of the systems, a series of equivalent preconditions are discussed in detail. After this, a Luenberger observer is designed for the augmented linear descriptor system to estimate both the state and the unknown input simultaneously. Besides, a high-order sliding mode differentiator is used to estimate the unknown information of the auxiliary output. Finally, a simulation example of a single-link flexible joint robotic is given to illustrate the effectiveness of the proposed method. © 2017, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.