Skip to main content
Log in

Mode-dependent IOSS Conditions for Continuous-time Switched Nonlinear Systems

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper investigates the input/output-to-state stability (IOSS) for continuous-time switched nonlinear systems (CTSNSs) containing both IOSS and non-IOSS constituent subsystems under mode-dependent average dwell time switching signal. New sufficient IOSS conditions are established to guarantee the IOSS properties of the CTSNSs, which extend the related existing results to a more general mode-dependent situation. A numerical example is provided to illustrate the effectiveness of the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. Liu, Z. Gong, E. Feng, and H. Yin, “Optimal switching control of a fed-batch fermentation process,” Journal of Global Optimization, vol. 52, no. 2, pp. 265–280, Feb. 2011.

    Article  MathSciNet  Google Scholar 

  2. C. Cassandras, D. Pepyne, and Y. Wardi, “Optimal control of a class of hybrid systems,” IEEE Transactions on Automatic Control, vol. 46, no. 3, pp. 398–415, Mar. 2001.

    Article  MathSciNet  Google Scholar 

  3. X. Xiao, L. Zhou, D. W. C. Ho, and G. Lu, “Event-triggered control of continuous-time switched linear systems,” IEEE Transactions on Automatic Control, vol. 64, no. 4, pp. 1710–1717, Apr. 2019.

    Article  MathSciNet  Google Scholar 

  4. X. Xiao, J. H. Park, L. Zhou, and G. Lu, “Event-triggered control of discrete-time switched linear systems with network transmission delays,” Automatica, vol. 111, p. 108585, Jan. 2020.

    Article  MathSciNet  Google Scholar 

  5. Y. Qi, P. Zeng, and W. Bao, “Event-triggered and self-triggered H control of uncertain switched linear systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 4, pp. 1442–1454, Apr. 2020.

    Article  Google Scholar 

  6. X. Xu, Y. Li, C. Liu, and H. Zhang, “Event-triggered control of discrete-time switched linear systems with an arbitrary sampling period,” International Journal of Control, Automation and Systems, vol. 19, no. 1, pp. 279–288, 2021.

    Article  Google Scholar 

  7. D. Du, Y. Yang, H. Zhao, and Y. Tan, “Robust fault diagnosis observer design for uncertain switched systems,” International Journal of Control, Automation and Systems, vol. 18, no. 12, pp. 3159–3166, 2020.

    Article  Google Scholar 

  8. Q. Su, H. Zhu, and J. Li, “Static output feedback stabilization of a class of switched linear systems with state constraints,” International Journal of Control, Automation and Systems, vol. 16, no. 2, pp. 505–511, Apr. 2018.

    Article  Google Scholar 

  9. L. Zhu, J. Qiu, and H. R. Karimi, “Region stabilization of switched neural networks with multiple modes and multiple equilibria: A pole assignment method,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 9, pp. 3280–3293, Sep. 2020.

    Article  MathSciNet  Google Scholar 

  10. X. Zhao, L. Zhang, P. Shi, and M. Liu, “Stability and stabilization of switched linear systems with mode-dependent average dwell time,” IEEE Transactions on Automatic Control, vol. 57, no. 7, pp. 1809–1815, Jul. 2012.

    Article  MathSciNet  Google Scholar 

  11. E. D. Sontag, “Smooth stabilization implies coprime factorization,” IEEE Transactions on Automatic Control, vol. 34, no. 4, pp. 435–443, Apr. 1989.

    Article  MathSciNet  Google Scholar 

  12. Z. Ai and G. Zong, “Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems,” Applied Mathematics and Computation, vol. 245, pp. 462–473, Oct. 2014.

    Article  MathSciNet  Google Scholar 

  13. Y. Liu, Y. Kao, H. R. Karimi, and Z. Gao, “Input-to-state stability for discrete-time nonlinear switched singular systems,” Information Sciences, vol. 358–359, pp. 18–28, Sep. 2016.

    Article  Google Scholar 

  14. B. Liu, D. J. Hill, and Z. Sun, “Input-to-state-KL-stability and criteria for a class of hybrid dynamical systems,” Applied Mathematics and Computation, vol. 326, pp. 124–140, Jun. 2018.

    Article  MathSciNet  Google Scholar 

  15. X. Qi, H. Bao, and J. Cao, “Exponential input-to-state stability of quaternion-valued neural networks with time delay,” Applied Mathematics and Computation, vol. 358, pp. 382–393, Oct. 2019.

    Article  MathSciNet  Google Scholar 

  16. F. Sun, L. Gao, W. Zhu, and F. Liu, “Generalized exponential input-to-state stability of nonlinear systems with time delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 44, pp. 352–359, Mar. 2017.

    Article  MathSciNet  Google Scholar 

  17. H. Zhu, P. Li, X. Li, and H. Akca, “Input-to-state stability for impulsive switched systems with incommensurate impulsive switching signals,” Communications in Nonlinear Science and Numerical Simulation, vol. 80, p. 104969, Jan. 2020.

    Article  MathSciNet  Google Scholar 

  18. E. D. Sontag and Y. Wang, “Output-to-state stability and detectability of nonlinear systems,” Systems & Control Letters, vol. 29, no. 5, pp. 279–290, Feb. 1997.

    Article  MathSciNet  Google Scholar 

  19. D. Liberzon, Switching in Systems and Control, Birkhäuser, Boston, 2003.

    Book  Google Scholar 

  20. L. Vu, D. Chatterjee, and D. Liberzon, “Input-to-state stability of switched systems and switching adaptive control,” Automatica, vol. 43, no. 4, pp. 639–646, Apr. 2007.

    Article  MathSciNet  Google Scholar 

  21. M. A. Müller and D. Liberzon, “Input/output-to-state stability and state-norm estimators for switched nonlinear systems,” Automatica, vol. 48, no. 9, pp. 2029–2039, Sep. 2012.

    Article  MathSciNet  Google Scholar 

  22. L. Zhang and H. Gao, “Asynchronously switched control of switched linear systems with average dwell time,” Automatica, vol. 46, no. 5, pp. 953–958, May 2010.

    Article  MathSciNet  Google Scholar 

  23. Y.-E. Wang, H. R. Karimi, and D. Wu, “Conditions for the stability of switched systems containing unstable subsystems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 66, no. 4, pp. 617–621, Apr. 2019.

    Article  Google Scholar 

  24. P. Cheng, J. Wang, S. He, X. Luan, and F. Liu, “Observer-based asynchronous fault detection for conic-type nonlinear jumping systems and its application to separately excited DC motor,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 67, no. 3, pp. 951–962, Mar. 2020.

    Article  MathSciNet  Google Scholar 

  25. P. Cheng, M. Chen, V. Stojanovic, and S. He, “Asynchronous fault detection filtering for piecewise homogenous Markov jump linear systems via a dual hidden Markov model,” Mechanical Systems and Signal Processing, vol. 151, p. 107353, Apr. 2021.

    Article  Google Scholar 

  26. P. Cheng, S. He, J. Cheng, X. Luan, and F. Liu, “Asynchronous output feedback control for a class of conic-type nonlinear hidden Markov jump systems within a finite-time interval,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1–8, 2020. DOI: https://doi.org/10.1109/TSMC.2020.2980312

  27. P. Cheng and S. He, “Observer-based finite-time asynchronous control for a class of hidden Markov jumping systems with conic-type non-linearities,” IET Control Theory & Applications, vol. 14, pp. 244–252, Jan. 2020.

    Article  Google Scholar 

  28. L. Liu, R.-W. Guo, and S.-P. Ma, “Input/output-to-state stability of switched nonlinear systems with an improved average dwell time approach,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 461–468, Apr. 2016.

    Article  Google Scholar 

  29. M. Krichman, E. D. Sontag, and Y. Wang, “Input-output-to-state stability,” SIAM Journal on Control and Optimization, vol. 39, no. 6, pp. 1874–1928, Jan. 2001.

    Article  MathSciNet  Google Scholar 

  30. W. Hu, Q. Zhu, and H. R. Karimi, “Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems,” IEEE Transactions on Automatic Control, vol. 64, no. 12, pp. 5207–5213, Dec. 2019.

    Article  MathSciNet  Google Scholar 

  31. Z.-M. Li, X.-H. Chang, and J. H. Park, “Quantized static output feedback fuzzy tracking control for discrete-time nonlinear networked systems with asynchronous event-triggered constraints,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 6, pp. 3820–3831, 2021.

    Article  Google Scholar 

  32. Z.-M. Li and J. H. Park, “Dissipative fuzzy tracking control for nonlinear networked systems with quantization,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 12, pp. 5130–5141, Dec. 2020.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lei Zhou.

Additional information

Recommended by Associate Editor Xiao-Heng Chang under the direction of Editor Jessie (Ju H.) Park.

This work was supported by the National Natural Science Foundation of China under Grant 62073181, and was also supported by China Scholarship Council (CSC NO. 201908320096), Jiangsu Overseas Visiting Scholar Program for University Prominent Young & Middle-aged Teachers and Presidents.

Xiaoqing Xiao is currently a Professor with the School of Information Science and Technology, Nantong University, Jiangsu, China. She received her Ph.D. degree from the School of Automation, Nanjing University of Science and Technology, Jiangsu, China, in 2017. She worked as a Postdoc at Department of Electrical Engineering, Yeungnam University, Korea, from 2017 to 2018. Her current research interests include event-triggered filtering and control, switched systems.

Lei Zhou received his Ph.D. degree from the Department of Mathematics, East China Normal University, China, in 2010. He joined Nantong University, Jiangsu, China, in 2004 and he is currently a Professor with the School of Information Science and Technology. From 2010 to 2019, he has visited the Department of Mathematics, City University of Hong Kong, Hong Kong, for several times as Research Associate, Senior Research Associate. In 2018, he was a Visiting Scholar with the Department of Electrical Engineering, Yeungnam University, Korea, for two months. From June 2019 to November 2020, he was a Visiting Scholar with Tandon School of Engineering, New York University, NY, USA. His current research interests include switched systems, singular systems and networked control systems.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiao, X., Zhou, L. Mode-dependent IOSS Conditions for Continuous-time Switched Nonlinear Systems. Int. J. Control Autom. Syst. 19, 3580–3587 (2021). https://doi.org/10.1007/s12555-020-0786-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-020-0786-x

Keywords

Navigation