Prescribed-Time Fault Estimation and Unknown Input Compensation by Using Periodic Delayed Approach

This article considers the design of prescribed-time sensor fault estimators (PSFEs) and unknown input compensation for linear systems, i.e., estimators that estimate the sensor fault and controllers that stabilize the state of the system both at a prescribed time. With this intention, a filter is introduced to eliminate the limitation of the fault being differentiable. Then, the task of designing PSFEs can be converted into the task of designing prescribed-time unknown input observers for the augmented systems. Next, the generalized inverse is employed to convert the augmented systems into a form suitable for observer design. Then, the PSFEs are developed by exploiting periodic delayed output. Both full-and reduced-order PSFEs are taken into account. In addition, based on the established state observer and unknown input estimation, periodic delayed controllers are designed to completely compensate for the unknown input so that the closed system is T-prescribed-time stable (T-PS). Finally, an example is provided to demonstrate the efficacy of the proposed methods.