Nonlinear Dynamics

, Volume 93, Issue 2, pp 847–862 | Cite as

Adaptive stabilization for a class of uncertain \({\textit{p}}\)-normal nonlinear systems via a generalized homogeneous domination technique

  • Xingchen Xu
  • Chuanlin Zhang
  • Qingshan Liu
  • Jinde Cao
  • Ahmed Alsaedi
Original Paper


This paper investigates a generalized homogeneous adaptive stabilization method for a class of high-order nonlinear systems without controllable/observable linearizations. Based on a general approximated homogeneous function restraining hypothesis, a series of quasi-homogeneous adaptive virtual controllers are built. By modifying the homogenous domination approach, an inductive stability analysis as well as the guideline of update laws is carried out in an explicit way. Furthermore, based on the proposed design framework, the asymptotical and finite-time stabilization with the flexibility of tuning homogeneous degree are investigated. Numerical simulations and a real example are presented to demonstrate the effectiveness of the proposed method.


Adaptive stabilization Homogenous system theory p-normal nonlinear system Recursive design 



Funding was provided by National Natural Science Foundation of China (Grant Nos. 61503236, 61473333, 61573096) and Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002).


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AutomationHuazhong University of Science and TechnologyWuhanChina
  2. 2.College of Automation EngineeringShanghai University of Electric PowerShanghaiChina
  3. 3.Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of MathematicsSoutheast UniversityNanjingChina
  4. 4.School of Electrical EngineeringNantong UniversityNantongChina
  5. 5.School of Mathematical SciencesShandong Normal UniversityJi’nanChina
  6. 6.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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