Observation for non-linear uncertain systems with multiple outputs via non-homogeneous high-order sliding modes

This article presents the problem of finite time state observation for a class of non-linear systems with multiple outputs affected by modeling uncertainties and unknown inputs. The proposed adaptable method is based on the non-homogeneous high-order sliding mode control approach. The observability is derived in terms of certain geometric restrictions on the vector fields of the system. A method for the exact reconstruction of the unknown inputs is stated. The method does not require the system to be transformed to any normal form. Simulation results support the proposed method.