Simultaneous estimation of multiple channel faults for two-dimensional linear systems

This study focuses on the problem of simultaneous estimation of multiple channel faults for two-dimensional linear systems, which are described by Fornasini–Marchesini second (FM-II) model, and the faults that exist in state equation and measurement equation. By transforming the fault in the measurement equation as augmented state, the FM-II model with faults in the state equation and measurement equation can be rewritten into a singular system. Hence, several observers are proposed for the singular systems, and then the estimation of the faults in the state equation and measurement equation can be obtained. Using Lyapunov stability theory, sufficient conditions for the existence of the asymptotically stable observer and uniformly ultimately bounded observer are derived in the context of time domain. For the bounded observer, the upper bound of estimation error can be provided referring to the fault bound. Numerical and practical examples are given to demonstrate the effectiveness of the proposed method.