AIMS Mathematics, 2021, 6(1): 102-113. doi: 10.3934/math.2021008.

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Exponential stability analysis and control design for nonlinear system with time-varying delay

College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, P. R. China

This paper investigates the problem of exponential stability analysis and control design for time delay nonlinear systems with unknown control coefficient. Nussbaum gain function is utilized to solve the problem of unknown control directions at every step. By designing a new Lyapunov-Krasovskii functional, the problem of unknown time-varying delay is solved. Under the frame of adaptive backstepping recursive design, an exponential stabilization control algorithm is developed, which demonstrates that all solutions of controlled system are ultimately uniformly bounded (UUB) and exponential converge to zero. Finally, simulation results are displayed to explain the superiority and effectiveness of the developed control method.
  Figure/Table
  Supplementary
  Article Metrics

Keywords exponential stabilization; time-varying delay; Nussbaum gain function backstepping recursive design

Citation: Xuelian Jin. Exponential stability analysis and control design for nonlinear system with time-varying delay. AIMS Mathematics, 2021, 6(1): 102-113. doi: 10.3934/math.2021008

References

  • 1. K. T. Yu, Y. M. Li, Adaptive fuzzy control for nonlinear systems with sampled data and time-varying input delay, AIMS Mathematics, 5 (2020), 2307-2325.
  • 2. X. L. Zhu, B. Chen, D. Yue, Y. Y. Wang, An improved input delay approach to stabilization of fuzzy systems under variable sampling, IEEE T. Fuzzy Syst., 20 (2011), 330-341.
  • 3. H. Li, L. Wang, H. Du, A. Boulkroune, Adaptive fuzzy backstepping tracking control for strictfeedback systems with input delay, IEEE T. Fuzzy Syst., 25 (2016), 642-652.
  • 4. C. Hua, G. Feng, X. Guan, Robust controller design of a class of nonlinear time delay systems via backstepping method, Automatica, 44 (2008), 567-573.
  • 5. S. S. Ge, F. Hong, T. H. Lee, Robust adaptive control of nonlinear systems with unknown time delays, Automatica, 41 (2005), 1181-1190.
  • 6. S. J. Yoo, Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form, Int. J. Syst. Sci., 48 (2017), 1347-1355.
  • 7. Y. Wen, X. Ren, Neural networks-based adaptive control for nonlinear time-varying delays systems with unknown control direction, IEEE T. Neural. Networ., 22 (2011), 1599-1612.
  • 8. Z. Yu, Y. Dong, S. Li, F. Li, Adaptive tracking control for switched strict-feedback nonlinear systems with time-varying delays and asymmetric saturation actuators, Neurocomputing, 238 (2017), 245- 254.
  • 9. S. Tong, Y. Li, Observer-based fuzzy adaptive robust control of nonlinear systems with time delays and unmodeled dynamics, Neurocomputing, 74 (2010), 369-378.
  • 10. S. Tong, X. Min, Y. Li, Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions, IEEE T. Cybernetics, 50 (2020), 3903-3913.
  • 11. S. S. Ge, J. Wang, Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients, IEEE T. Automat. Contr., 48 (2003), 1463-1469.
  • 12. S. Tong, S. Sui, Y. Li, Adaptive fuzzy decentralized output stabilization for stochastic nonlinear large-scale systems with unknown control directions, IEEE T. Fuzzy Syst., 22 (2013), 1365-1372.
  • 13. Y. Li, S. Tong, T. Li, Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones, IEEE T. Fuzzy Syst., 23 (2014), 1228-1241.
  • 14. R. T. M'Closkey, R. M. Murray, Exponential stabilization of driftless nonlinear control systems using homogeneous feedback, IEEE T. Automat. Contr., 42 (1997), 614-628.
  • 15. Z. P. Jiang, Robust exponential regulation of nonholonomic systems with uncertainties, Automatica, 36 (2000), 189-209.
  • 16. Z. Xi, G. Feng, Z. P. Jiang, D. Cheng, Output feedback exponential stabilization of uncertain chained systems, J. Franklin I., 344 (2007), 36-57.
  • 17. C. C. Hua, Q. G. Wang, X. P. Guan, Exponential stabilization controller design for interconnected time delay systems, Automatica, 44 (2008), 2600-2606.
  • 18. X. Qin, Adaptive exponential stabilization for a class of stochastic nonholonomic systems, Abstr. Appl. Anal., 2013 (2013), 1-6.
  • 19. W. Chen, C. Wen, J. Wu, Global exponential/finite-time stability of nonlinear adaptive switching systems with applications in controlling systems with unknown control direction, IEEE T. Automat. Contr., 63 (2018), 2738-2744.
  • 20. X. Li, Donal O'Regan, H. Akca, Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays, IMA J. Appl. Math., 80 (2015), 85-99.
  • 21. D. Yang, X. Li, J. Qiu, Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback, Nonlinear Anal-Hybri., 32 (2019), 294-305.
  • 22. D. Yang, X. Li, J. Shen, Z. Zhou, State-dependent switching control of delayed switched systems with stable and unstable modes, Math. Method. Appl. Sci.,41 (2018), 6968-6983.
  • 23. J. Hu, G. Sui, X. Lv, X. Li, Fixed-time control of delayed neural networks with impulsive perturbations, Nonlinear Anal-Model., 23 (2018), 904-920.
  • 24. J. Zhai, H. R. Karimi, Universal adaptive control for uncertain nonlinear systems via output feedback, Inform. Sciences, 500 (2019), 140-155.
  • 25. J. Y. Zhai, Dynamic output-feedback control for nonlinear time-delay systems and applications to chemical reactor systems, IEEE T. Circuits-II, 66 (2019), 1845-1849.
  • 26. S. C. Tong, Y. M. Li, Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties, Sci. China Inform. Sci., 53 (2010), 307-324.
  • 27. S. C. Tong, Y. M. Li, Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems, Sci. China Inform. Sci., 57 (2014), 1-14.

 

Reader Comments

your name: *   your email: *  

© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved