A sliding mode observer for fault reconstruction under output sampling: A time-delay approach

A sliding mode observer in the presence of sampled output information and its application to fault reconstruction is studied. The observer is designed by using the delayed continuous-time representation of the sampled-data system, for which a set of Linear Matrix Inequalities (LMIs) provide conditions for the ultimate boundedness. It is shown that an ideal sliding motion cannot be achieved in the observer when outputs are sampled. However, ultimately bounded solutions can be obtained provided the sampling frequency is fast enough. The bound on the solution is proportional to the sampling time and the magnitude of the switching gain. The proposed observer design is applied to the problem of fault reconstruction under sampled output. It is shown that, for a sufficiently small value of μ, a perturbation parameter, a transducer or sensor fault can be reconstructed reliably from the output error dynamics. An example of observer design for an inverted pendulum system is used to demonstrate the merit of the proposed methodology compared to existing sliding mode observer design approaches.