Zonotopic Fault Detection Observer with H− Performance

This paper proposes a robust fault detection observer based on zonotopes for discrete-time uncertain systems with sensor faults and unknown but bounded uncertainties. The main advantage of this method is that the observer gain of the robust zonotopic observer is designed to be robust against bounded uncertainties while being sensitive to faults. In order to detect sensor faults with low magnitudes, the fault sensitivity is taken into account by measuring the H− performance. The designed zonotopic observer gain can be obtained by solving an optimization problem including a sequence of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the proposed method.