Nonlinear Dynamics

, Volume 94, Issue 4, pp 2889–2899 | Cite as

Fixed-time stabilization of high-order integrator systems with mismatched disturbances

  • Bailing TianEmail author
  • Hanchen Lu
  • Zongyu Zuo
  • Hong Wang
Original Paper


The fixed-time stabilization of high-order integrator systems with both matched and mismatched disturbances is investigated. A continuous non-switching control law is designed based on the bi-limit homogeneous technique for arbitrary-order integrator systems. Combining with fixed-time disturbance observer, the proposed continuous control law for the system with matched and mismatched disturbances guarantees that the convergence time is uniformly bounded with respect to any initial states. Finally, the numerical results are provided to verify the efficiency of the developed method.


Fixed-time stability Disturbance observer Mismatched disturbances 



The work was done when the authors were with the University of Manchester, UK, and it was supported in part by the National Natural Science Foundation of China (Grant Nos. 61673034, 61673294 and 61773278) and in part by the Ministry of Education Equipment Development Fund under Grant Nos. 6141A02033311 and 6141A02022328.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Electrical and Information EngineeringTianjin UniversityTianjinChina
  2. 2.School of Automation Science and Electrical EngineeringBeihang University (BUAA)BeijingChina
  3. 3.School of Electrical and Electronic EngineeringThe University of ManchesterManchesterUK

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