Observer-based fault-tolerant control for non-infinitely observable descriptor systems with unknown time-varying state and input delays

This paper presents a fault-tolerant control (FTC) scheme for a class of non-infinitely observable descriptor systems (NIODS) that is affected by unknown time-varying state and input delays. The NIODS is first transformed into a form facilitating the manipulation of design freedom inherent in its structure. Some of the system states are then treated as unknown inputs to form an infinitely observable reduced-order system. A sliding mode observer (SMO) is applied to estimate the states and faults based on measurable signals. Next, a memoryless controller is designed using these estimates. Design conditions for the SMO and controller are derived in the form of linear matrix inequalities. In the case where the state and input delays are different, the FTC scheme is designed to limit the effect of the mismatch in delays on the output. In the case of equivalent state and input delays, the FTC scheme is designed so that the system output asymptotically converges to zero. A simulated example is lastly performed to verify the scheme’s effectiveness.