Adaptive observer design for unmatched faults estimation: A parametrization-based LMI method

In this paper, we address the problem of adaptive observer design for state and fault estimation. The concerned faulty plants are nonlinear and characterized by a structure that does not meet the well-known observer matching condition. A simple two-stage adaptive law, which does not require putting the system into any canonical form, is given to estimate the fault vector. Moreover, for efficient computation of the observer gains, a matrix parameterization approach is proposed to turn the sufficient stability conditions into a single linear matrix inequality. Finally, the model of a mechanical system is used to test the applicability and effectiveness of the presented scheme.