Abstract: This paper is concerned with the problem of estimating the states for a kind of linear systems unknown inputs when the so-called matching condition was not satisfied. Employing the concept of the relative degree of the system, the auxiliary output vector which may satisfy the observer matching condition was constructed. Based on the auxiliary output vector, a reduced-order observer approach was proposed. The high-gain observers were used to estimate auxiliary output vector. Then, instead of auxiliary output vector, by employing its estimation, a reduced-order observer was constructed. The state estimation error is shown to be uniformly and ultimately bounded with respect to a ball whose radius can be adjusted by design parameters. The design method was declared and carried out with an illustrative example of a fiveorder model. The comparison between estimation performance of the sliding observer and reduced-order observer shows that the latter has the same good performance as the former.

Key words: observer matching condition； high-gain observer； reduced-order observer; , unknown input