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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 8217126, 15 pages
https://doi.org/10.1155/2017/8217126
Research Article

Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI

1School of Information Sciences and Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China
2School of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China

Correspondence should be addressed to Yude Ji; moc.361@eduy_ij

Received 13 February 2017; Revised 4 June 2017; Accepted 17 July 2017; Published 28 August 2017

Academic Editor: Michele Betti

Copyright © 2017 Jing Qiu and Yude Ji. 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.

Abstract

We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying . Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finsler’s Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.