Asymptotically stable observer for two-dimensional systems with multiple-channel faults

This paper proposes a novel observer design method for two dimensional systems with multiple channel faults. The two-dimensional systems are described by Fornasini-Marchesini local state-space second model (FM-II) and the faults exist in both state equation and measurement equation. This study considers two fault situations, according to whether the faults have the same source. By transforming the fault in measurement equation as augmented state, the FM-II model with faults can be rewritten into singular systems. Hence, two observers are proposed for the singular systems, and then the estimation of the faults can be obtained. The necessary and sufficient conditions for the existence of asymptotically stable observer are derived. Numerical examples are given to demonstrate the effectiveness of the proposed method.