Nested backward compensation of unmatched effects of unknown inputs based on HOSM identification

The paper considers 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. It is introduced a controller with a compensation strategy based on the identified perturbation values. When the system satisfies quite restrictive assumptions, the method ensures exact regulation of the unmatched states. In order to deal with the general case it is proposed a nested backward strategy to design the sliding surface, 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.