Joint unknown input observer for descriptor system based on interval observer

In this paper, a novel joint unknown input observer (JUIO) is proposed for a class of descriptor systems. The unknown input (UI) to be estimated injects additively into both the state and output equations in a state space model. To the best of our knowledge, only a few contributions in existing work address this problem directly. To begin with, by introducing an auxiliary UI, the original system is transformed into a normal form in which the output is no longer affected by UI. In this way, the negative effect brought by the UI occurring in the output measurement is removed. An interval observer is developed to obtain upper and lower boundary estimates of the output of the reformulated system. After that, an algebraic relationship between the auxiliary UI and the states is established, and a UI reconstruction (UIR) method is developed. Based on the UIR, a JUIO comprising the UIR and a Luenberger-like state observer is developed to achieve asymptotic estimations of the UI and state simultaneously. Verifiable conditions for the existence of the proposed JUIO are given with respect to the original descriptor system. Finally, a simulation example is presented to verify the effectiveness of the proposed method.