Observer design for systems with unknown inputs and missing measurements

In this paper, the observer design problem is considered for a class of systems with unknown inputs and missing measurements. A Bernoulli distributed sequence taking values on 0 or 1 is employed to govern possible missing measurements. It is worth mentioning that the effects of the unknown inputs cannot be fully eliminated from the estimation error due to the stochastic nature of the addressed system. In such a case, an observer is established which can decouple the estimation error from the unknown inputs in the mathematical expectation sense. Moreover, the uniform ultimate boundedness of the estimation error is discussed. A simulation example is presented to show the effectiveness of the proposed algorithm.