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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 9730312, 14 pages
https://doi.org/10.1155/2017/9730312
Research Article

Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

1School of Computer Engineering, Jinling Institute of Technology, Nanjing 211169, China
2School of Mathematics, Pingdingshan Institute of Education, Pingdingshan 467000, China
3School of Mathematics and Physics, Henan University of Urban Construction, Pingdingshan 467000, China

Correspondence should be addressed to Qixun Lan; nc.ude.jcnh@nal.q

Received 13 July 2016; Accepted 15 January 2017; Published 15 February 2017

Academic Editor: Rigoberto Medina

Copyright © 2017 Xiaohui Mo 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.

Abstract

In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs) subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC) is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC) law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO) is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.