Global hierarchical observer for linear systems with unknown inputs

A sliding-mode based observer is suggested in order to achieve global, finite-time reconstruction of the state vector for a class of linear systems with unknown inputs. In the paper we show that, by using a recently proposed global second-order sliding mode differentiation algorithm, the necessary and sufficient structural conditions for the observer design are preserved, with respect to previous works; meanwhile, the class of allowed unknown inputs is generalized significantly. A numerical example illustrates the effectiveness of the suggested technique.