Nonlinear Dynamics

, Volume 83, Issue 4, pp 2509–2522 | Cite as

Stability analysis and constrained fuzzy tracking control of positive nonlinear systems

  • Xiaolong Zheng
  • Xinyong Wang
  • Yunfei Yin
  • Lili Hu
Original Paper


This paper is concerned with stability and tracking control of positive nonlinear systems via Takagi–Sugeno (T–S) fuzzy modeling. Firstly, some less conservative stability conditions for positive nonlinear systems that can be represented by a class of positive T–S fuzzy model with only nonnegative state variables are derived by proposing the so-called quadratic copositive Lyapunov functions. Secondly, a constrained control via the parallel distributed compensation scheme is designed to stabilize a positive nonlinear system, while imposing positivity in closed loop, upon which a constrained fuzzy tracking controller is also given to guarantee the tracking performance and positivity in closed loop. Finally, a numerical example is provided to show the advantages of the proposed methods, and an example of a real plant is presented to demonstrate the controller design scheme.


Positive nonlinear systems T–S fuzzy system Quadratic copositive Lyapunov function Constrained tracking control 



This work was partially supported by the National Natural Science Foundation of China (61203123) and the Shandong Provincial Natural Science Foundation, China (ZR2012FQ019).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Xiaolong Zheng
    • 1
    • 2
  • Xinyong Wang
    • 1
    • 2
  • Yunfei Yin
    • 1
    • 2
  • Lili Hu
    • 1
    • 2
  1. 1.College of EngineeringBohai UniversityJinzhouChina
  2. 2.Chongqing SANY High-Intelligent Robots Co. Ltd.ChongqingChina

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