Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

This article highlights the interest of step-by-step higher order sliding mode observers for Multi-Input Multi-Output (MIMO) nonlinear systems with unknown inputs. A structural matching condition, commenting on the possibility to design such observers and to reconstruct the unknown inputs, is derived. A finite time sliding mode observer, based on the hierarchical use of the super twisting algorithm, is developed. Then, it is shown that this observer is of interest in the field of hybrid systems and systems with observability singularities. Lastly, it is shown through an example how to relax the usual matching condition by the means of this type of finite time sliding mode observer.