Discontinuous dynamical systems for fault detection. A unified approach including fractional and integer order dynamics

This paper considers a discontinuous dynamical observers stack and presents its possible application in the framework of fault detection and isolation (FDI) problems. Non-standard forms for the discontinuous observer injection signals, based on second-order sliding-mode techniques with dynamical sliding manifolds, are employed in the present work. A unified treatment covering at the same time integer-order and fractional-order (FO) dynamics is developed. Appropriate non-smooth Lyapunov analysis is made to support the theoretical properties of the suggested FDI observers, which yields simple tuning formulas for the corresponding parameters. Numerical implementation aspects are discussed. Finally, simulation and experimental results are presented to support the theoretical treatment, which confirm the expected performance.