Asymptotic convergence unknown input observer design via interval observer

In this paper, for a linear system with unknown input, a novelty unknown input observer (UIO) which can produce the asymptotic system state estimation and unknown input reconstruction simultaneously via interval observer is developed. Firstly, under the assumption that the boundary of the unknown input is known, the interval estimation of the output vector is obtained by designing an interval observer. Secondly, by using the upper and lower boundary estimations of the output vector, an algebraic relationship between the unknown input and the system state is set up. Thirdly, based on the algebraic relationship, a Luenberger-like state observer together with an algebraic unknown input reconstruction is designed to form a UIO. Moreover, a UIO is designed for a time-delay system with unknown input by applied the proposed UIO on the time-delay system directly, showing the advantages of the proposed UIO. Finally, simulation examples and some comparisons to the existing results are given to illustrate the effectiveness and advantages of the proposed method.