Prescribed-time sensor fault estimation for linear systems with unknown inputs by periodic delayed observers

This paper studies the problem of sensor fault estimation for linear systems in the presence of unknown inputs in both input and output channels. Relying on matrix equation theory, the unknown inputs are first removed from the output channel. Second, an augmented descriptor system is constructed by treating both system state and sensor fault as (pseudo)-state variables. Third, the augmented descriptor system is transformed into a regular one, followed by the elimination of the unknown input from the state equation. Finally, a reduced-order prescribed-time sensor fault estimator is obtained by using periodic delayed observers. This matrix equation based approach is then complemented by an alternative one, which relies on successive transformations of state, input and outputs. This approach sheds light on the adopted solvability conditions throughout the paper and on the role of different directions in the output space in handling unknown inputs, sensor faults and the core state estimation problem. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed methodologies.