Output nested backward compensation of unmatched effects of unknown inputs

This paper tackles the regulation problem of linear time invariant systems with unmatched perturbations. The proposed methodology exploits a high order sliding mode observer, which guarantees theoretically exact state and perturbation estimation. In this work is introduced a controller with a compensation strategy based on the identified perturbation values. A nested backward sliding surface design is proposed, which allows to compensate the unmatched uncertainties and to stabilize some of the non-actuated state components, while all the remaining states are maintained bounded. The overall stabilization error is estimated in terms of the sampling time and actuator time constant values. The feasibility of the technique is showed in a rotary inverted pendulum simulation example.