Finite-time Stabilization with Output-constraints of A Class of High-order Nonlinear Systems

  • Ruicheng Ma
  • Bin Jiang
  • Yan Liu
Regular Papers Control Theory and Applications


In this paper, the finite-time stabilization with output-constraint is investigated for a class of high-order nonlinear systems with the powers of positive odd rational numbers by constructing a Barrier Lyapunov function. First, sufficient conditions on characterizing the nonlinear functions of the considered systems are derived. Then, based on the technique of adding one power integrator, the global finite-time stabilizers of individual subsystems are systematically constructed to guarantee global finite-time stability with output constraints of the closed-loop nonlinear system. Finally, an example is provided to demonstrate the effectiveness of the proposed result.


Adding one power integrator barrier Lyapunov function finite-time stabilization high-order nonlinear systems output constraint 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Chang, Y.-M. Fang, L. Liu, and K.-S. Kang, “Prescribed performance adaptive neural tracking control for strict-feedback markovian jump nonlinear systems with time-varying delay,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1020–1031, Jun 2017. [click]CrossRefGoogle Scholar
  2. [2]
    R. Ma, Y. Liu, S. Zhao, and J. Fu, “Finite-time stabilization of a class of output-constrained nonlinear systems,” Journal of the Franklin Institute, vol. 352, no. 12, pp. 5393–6018, 2015.MathSciNetCrossRefGoogle Scholar
  3. [3]
    H. Li, L. Wang, H. Du, and A. Boulkroune, “Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 3, pp. 642–652, 2017. [click]CrossRefGoogle Scholar
  4. [4]
    R. Ma and J. Zhao, “Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings,” Automatica, vol. 46, no. 11, pp. 1819–1823, 2010. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    W. Lin and C. Qian, “Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems,” Systems & Control Letters, vol. 39, no. 5, pp. 339–351, 2000. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Z. Y. Sun, C. H. Zhang, and Z. Wang, “Adaptive disturbance attenuation for generalized high-order uncertain nonlinear systems,” Automatica, vol. 80, pp. 102–109, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 1, pp. 751–766, 2000. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    G. He and Z. Geng, “Finite-time stabilization of a combdrive electrostatic microactuator,” IEEE/ASME Transactions on Mechatronics, vol. 17, no. 1, pp. 107–115, 2012.CrossRefGoogle Scholar
  9. [9]
    J. Fu, R. Ma, and T. Chai, “Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers,” Automatica, vol. 54, no. 4, pp. 360–373, 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    H. Shen, J. H. Park, Z. G. Wu, and Z. Zhang, “Finitetime H∞ synchronization for complex networks with semimarkov jump topology,” Communications in Nonlinear Science and Numerical Simulation, vol. 24, no. 1–3, pp. 40–51, 2015. [click]MathSciNetCrossRefGoogle Scholar
  11. [11]
    H. Shen, J. Park, and Z.-G. Wu, “Finite-time reliable L 2-L∞=H∞ control for takagi-sugeno fuzzy systems with actuator faults,” IET Control Theory & Applications, vol. 8, no. 9, pp. 688–696, 2014. [click]MathSciNetCrossRefGoogle Scholar
  12. [12]
    J. Cheng, J. H. Park, L. Zhang, and Y. Zhu, “An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 11, pp. 6–18, 2016.Google Scholar
  13. [13]
    J. Cheng, H. P. Ju, Y. Liu, Z. Liu, and L. Tang, “Finitetime H∞ fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions,” Fuzzy Sets & Systems, vol. 314, pp. 99–115, 2016.CrossRefzbMATHGoogle Scholar
  14. [14]
    M. Burger and M. Guay, “Robust constraint satisfaction for continuous-time nonlinear systems in strict feedback form,” IEEE Transactions on Automatic Control, vol. 55, no. 11, pp. 2597–2601, 2010. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    K. P. Tee, S. S. Ge, and F. E. H. Tay, “Adaptive control of electrostatic microactuators with bidirectional drive,” IEEE transactions on control systems technology, vol. 17, no. 2, pp. 340–352, 2009. [click]CrossRefGoogle Scholar
  16. [16]
    S. Huang and Z. Xiang, “Finite-time stabilization of a class of switched nonlinear systems with state constraints,” International Journal of Control, pp. 1–24, 2017.Google Scholar
  17. [17]
    X. Huang, W. Lin, and B. Yang, “Global finite-time stabilization of a class of uncertain nonlinear systems,” Automatica, vol. 41, no. 5, pp. 881–888, 2005. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    B. Ren, S. S. Ge, K. P. Tee, and T. H. Lee, “Adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function,” IEEE Transactions on Neural Networks, vol. 21, no. 8, pp. 1339–1345, 2010. [click]CrossRefGoogle Scholar
  19. [19]
    J. Back, S. G. Cheong, H. Shim, and J. H. Seo, “Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin,” Systems & Control Letters, vol. 56, no. 11–12, pp. 742–752, 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    R. Marino and P. Tomei, “Global adaptive output-feedback control of nonlinear systems. i. linear parameterization,” IEEE Transactions on Automatic Control, vol. 38, no. 1, pp. 17–32, 1993. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    B. Wang, J. Cheng, A. Al-Barakati, and H. M. Fardoun, “A mismatched membership function approach to sampleddata stabilization for T-S fuzzy systems with time-varying delayed signals,” Signal Processing, vol. 140, pp. 161–170, 2017.CrossRefGoogle Scholar
  22. [22]
    J. Cheng, H. P. Ju, H. R. Karimi, and X. Zhao, “Static output feedback control of nonhomogeneous Markovian jump systems with asynchronous time delays,” Information Sciences, vol. 399, pp. 219–238, 2017. [click]CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsLiaoning UniversityShenyangChina
  2. 2.College of Information Science & EngineeringNortheastern UniversityShenyang, LiaoningChina

Personalised recommendations