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Mathematical Problems in Engineering
Volume 2017, Article ID 3146231, 8 pages
Research Article

Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

1Electrical and Electronic Engineering Department, Autonomous University of Tamaulipas, Reynosa-Rodhe Campus, Reynosa, TAMPS, Mexico
2Robotic and Advanced Manufacturing Department, Research Center for Advanced Studies, Saltillo Campus, Ramos Arizpe, COAH, Mexico

Correspondence should be addressed to Aldo-Jonathan Muñoz-Vázquez; moc.liamg@zeuqzav.zonum.odla

Received 23 June 2017; Revised 16 August 2017; Accepted 29 August 2017; Published 8 October 2017

Academic Editor: Bogdan Dumitrescu

Copyright © 2017 Aldo-Jonathan Muñoz-Vázquez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii) continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.