Discrete‐time <i>H</i>₋ ∕ <i>H</i>_∞ sensor fault detection observer design for nonlinear systems with parameter uncertainty

SUMMARY This work concerns robust sensor fault detection observer (SFDO) design for uncertain and disturbed discrete‐time Takagi–Sugeno (T–S) systems using H − ∕ H ∞ criterion. The principle of the proposed approach is based on simultaneously minimizing the perturbation effect and maximizing the fault effect on the residual vector. Furthermore, by introducing slack decision matrices and taking advantage of the descriptor formulation, less conservative sufficient conditions are proposed leading to easier linear matrix inequalities (LMIs). Moreover, the proposed (SFDO) design conditions allow dealing with unmeasurable premise variables. Finally, a numerical example and a truck–trailer system model are proposed to illustrate the efficiency of the SFDO design methodology. Copyright © 2013 John Wiley &amp; Sons, Ltd.