Output derivative free design of unknown input plus state functional observer

We consider problem of state function as well as unknown input estimation using only measured outputs of a linear time-invariant system. Two separate reduced-order input estimators using the same design methodology are proposed. The first is an extension of the full-order state/input estimator previously reported in the literature. The second is based on the adaptive observer technique. The main achievement of the paper is that our proposed observer estimates a function of the state as opposed to the actual state, and as a result can be designed under less restrictive conditions than that of the state observers. Also, the proposed observer can be designed for certain non-minimum phase systems