Hierarchical observer for strongly detectable systems via second order sliding mode

Based on the concept of strong detectability, and its relation with the concept of invariant zeros, it is seen that the condition of strong detectability is a necessary and sufficient condition for the estimation of the state vector of a system with unknown inputs appearing explicitly in both places, the plant and the output of the system. We suggest a hierarchical scheme for the design of an observer whose trajectories converge to those of the original vector state. For the realization of such observer we take advantage of the properties of the second-order super-twisting sliding-mode algorithm, which is used as a substitute of a differentiator. We give a numerical example that illustrates the designing scheme proposed here.