Observer for linear time invariant systems with unknown inputs based on the hierarchical super-twisting concept

We use an algorithm, which allows to find the strong observable space, to design a hierarchical observer providing the exact reconstruction of the state components. In order to design the state estimation, we use the super twisting (second order sliding mode) algorithm. The continuity of the super twisting output injection allows to reconstruct in each step a vector formed by a matrix pre-multiplied by the state vector, all this in a finite time. The sequential application of this procedure finally leads to the obtaining of the state vector which can be represented by an auxiliary state vector plus the equivalent super twisting output injection. It is assumed only that the system has no zeros and the unknown inputs are bounded. A numerical example illustrates the efficiency of the suggested technique.