**5. Conclusions**

This paper has presented a passive fault-tolerant controller for a 3 degree of freedom mechanical crane. First, a convex model of the 3 DOF crane has been proposed, representing the nonlinear dynamic by a set of linear models interpolated by nonlinear weighting functions. Then, a tracking fault-tolerant controller with H ∞ performance criteria has been developed over the nonlinear states' trajectories. The H ∞ performance guarantees robustness against measurement noise and partial faults. The numerical simulations results show the effectivity of the proposed method by tracking a predefined position of the cart and the load while the oscillations are attenuated despite the actuator faults. Future work will investigate the inclusion of measurement noise and will compare the development with a full nonlinear controller such as a nonlinear or sliding model controller.

**Author Contributions:** Conceptualization, F.-R.L.-E. and S.G.-P.; formal analysis, O.S.-E. and C.H.-G.; methodology, F.-R.L.-E. and G.V.-P.; software O.S.-E. and S.G.-P.; validation G.V.-P. and C.H.-G.; writing—original draft preparation, F.-R.L.-E. and G.V.-P.; writing—review and editing, S.G.-P. and O.S.-E. All authors have read and agreed to the published version of the manuscript.

**Funding:** The Consejo Estatal de Ciencia y Tecnológia del Estado de Chiapas financed this project under the gran<sup>t</sup> number 1123. Aditional funding was provided from Conacyt, grants Projects 88 and 2759; and Tecnológico Nacional de México, grants 7641.20-P and 8017.20-P.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
