A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions

In this paper, a novel sliding mode observer is proposed for systems that do not satisfy common conditions required for fault estimation, in particular the so-called matching condition and minimum phase condition. Other works attempt to circumvent the matching condition by using multiple observers in cascade, or higher order sliding modes, whilst the minimum phase condition can be relaxed at the cost of some faults and the states being not estimated, or the fault estimation being corrupted by the fault time derivative (or other dynamics). For the proposed scheme in this paper, only one observer is required, the minimum phase condition is relaxed to detectability, and the matching condition is greatly simplified to a condition related to the system dimensions which makes the scheme also applicable to the case where there are less outputs than faults. Finally, a simulation example is conducted to verify the effectiveness of the proposed observer.