Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are

generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters.