Hierarchical Second-Order Sliding-Mode Observer for Linear 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 an observer for linear systems with bounded unknown inputs. To realize the observation of the state, a second order sliding mode observer is suggested. Such observer provides a robust estimate of the state vector in a finite time. The design is based on the concept of the hierarchical output injection maintaining a value of zero for output tracking error at each level of the hierarchy. The equivalent control is used to identify the unknown inputs, which can be used as a contribution concerning the problem of fault detection. A numerical example illustrates the effectiveness of the suggested technique