Unbounded unknown inputs estimation based on high-order sliding mode differentiator

An observer is designed for strongly detectable systems with unbounded unknown inputs. The design scheme is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as new states. Then, using a high-order sliding mode differentiator (HOSMD), a new output of the system is generated in order to fulfill the Hautus condition. Finally, the system is decomposed into two subsystem, the first one being unaffected directly by the unknown inputs, and the second subsystem being obtained directly from the system output. Thus, a Luenberger observer is designed for the first subsystem. This procedure allows one to estimate the state and the unknown inputs using the least number of differentiations possible. Some simulations are given to show the effectiveness of the proposed observer.