Hierarchical second-order sliding-mode observer for linear time invariant systems with unknown inputs

The problem of observability for systems with unknown inputs is revised. The sufficient and necessary conditions are used for the design of an observer for linear systems with bounded unknown inputs. To realize the observation of the state, a second-order sliding-mode observer is suggested to be applied. Such an observer provides a robust estimate of the state vector in a finite time, without filtration. The design is based on the concept of the hierarchical output injection maintaining zero value for output tracking error at each level of the hierarchy. The equivalent control is used to identify the unknown inputs. A numerical example illustrates the effectiveness of the suggested technique.