Finite-time observer design for singular systems subject to unknown inputs

This study is concerned with the finite-time observer (FTO) design for a class of singular systems subject to unknown inputs in both the state and the output equations. First, in order to overcome the restriction of the classical FTO method, two different non-singular auxiliary dynamic systems, which are simultaneously equivalent to the original singular system, are constructed to act as the new reference systems for the sub-observers' design. Second, based on the observer matching condition and strong observability condition, it is proven that an FTO can be designed where the observer parameters are given by an algebraic method. Also, in order to present a systematical method to compute the observer parameters, an alternative linear matrix inequality method is proposed. The advantages of the FTO over the conventional asymptotic convergence observer are discussed and numerical examples are given to show the effectiveness of the proposed method.