Skip to main content
SpringerLink
Log in

Stability Analysis and Control Synthesis for a Class of Cascade Switched Nonlinear Systems with Actuator Saturation

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper considers the stabilization problem for a class of cascade switched nonlinear systems. Each subsystem of the switched nonlinear system studied consists of a linear part and a nonlinear part, and the linear parts are composed of stabilizable and unstabilizable subsections. The actuator saturation is taken into consideration using the convex hull technique. Through constructing the proper Lyapunov functions, sufficient conditions in terms of LMIs for the solvability of the stabilization problem are presented. A state feedback controller and the dwell-time switching strategy are proposed to guarantee the exponential stability of the resulting closed-loop system. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed results.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. M.S. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Y.G. Chen, S.M. Fei, K.J. Zhang, L. Yu, Control of switched linear systems with actuator saturation and its applications. Math. Comput. Model. 56, 14–26 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Y.G. Chen, S.M. Fei, K.J. Zhang, Z.M. Fu, Control synthesis of discrete–time switched linear systems with input saturation based on minimum dwell time approach. Circuits Syst. Signal Process 31, 779–795 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. K.D. Do, Control of nonlinear systems with output tracking error constraints and its application to magnetic bearings. Int. J. Control 83(6), 1199–1216 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Lian, P. Shi, Z. Feng, Passivity and passification for a class of uncertain switched stochastic time-delay systems. IEEE Trans. Cybern. 43(1), 3–13 (2013)

    Article  Google Scholar 

  6. D. Liberzon, Switching in systems and control (Birkhaser, Boston, 2003)

    Book  MATH  Google Scholar 

  7. L. Lu, Z.L. Lin, H.J. Fang, L2 gain analysis for a class of switched systems. Automatica 45, 965–972 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. L. Lu, Z.L. Lin, A switching anti-windup design using multiple Lyapunov functions. IEEE Trans. Autom. Control 55, 142–148 (2010)

    Article  MathSciNet  Google Scholar 

  9. K.S. Narendra, J. Balakrishnan, A common lyapunov function for stable LTI systems with commuting A-matrices. IEEE Trans. Automat. Control 39(12), 2469–2471 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. W. Ni, D.Z. Chen, Control of switched linear systems with input saturation. Int. J. Syst. Sci. 41(9), 1057–1065 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Niu, J. Zhao, Output tracking control for a class of switched non-linear systems with partial state constraints. IET Control Theory Appl. 7(4), 623–631 (2013)

    Article  MathSciNet  Google Scholar 

  12. B. Niu, J. Zhao, Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems. Syst. Control Lett. 62(10), 963–971 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  13. X.M. Sun, G.P. Liu, D. Rees, W. Wang, Delay-dependent stability for discrete systems with large delay sequence based on switching techniques. Automatica 44, 2902–2908 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Wang, P. Shi, J.L. Wang, W. Wang, Delay-dependent exponential H-Infinity filtering for discrete-time switched delay systems. Int. J. Robust Nonlinear Control 22(13), 1522–1536 (2012)

    Article  MATH  Google Scholar 

  15. M. Wang, J. Zhao, L2-gain analysis and control synthesis for a class of uncertain switched nonlinear systems. Acta Automat. Sinica 35(11), 1459–1464 (2009)

    MathSciNet  Google Scholar 

  16. H. Yang, B. Jiang et al., Stabilization of switched nonlinear systems with all unstable modes: application to multi-agent systems. IEEE Trans. Autom. Control 56(9), 2230–2235 (2011)

    Article  MathSciNet  Google Scholar 

  17. X.Q. Zhang, M.S. Wang, J. Zhao, Stability analysis and anti-windup design of uncertain discrete-time switched linear systems subject to actuator saturation. Control Theory Appl. 10(3), 325–331 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Zhao, D.J. Hill, On stability, L\(_{2}\)-gain and \(H_{\infty }\) control for switched systems. Automatica 44, 1220–1232 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. X.D. Zhao, L.X. Zhang, P. Shi, M. Liu, Stability of switched positive linear systems with average dwell time switching. Automatica 48(6), 1132–1137 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. X.D. Zhao, L.X. Zhang, P. Shi, M. Liu, Stability and stabilization of switched linear systems with mode dependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2012)

    Article  MathSciNet  Google Scholar 

  21. X.D. Zhao, X.W. Liu, Improved results on stability of continuous-time switched linear systems. Automatica 50(2), 614–621 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants 61233002 and 61174073, and IAPI Fundamental Research Funds under Grant 2013ZCX03-01, and the Fundamental Research Funds for the Central Universities under Grand N120404019.

Author information

Authors and Affiliations

  1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, People’s Republic of China

    Juan Wang & Jun Zhao

  2. College of Information Science and Engineering, Northeastern University, Shenyang , 110819, People’s Republic of China

    Juan Wang & Jun Zhao

  3. College of Science, Tieling Normal College, Tieling , 112000, People’s Republic of China

    Juan Wang

Authors
  1. Juan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J., Zhao, J. Stability Analysis and Control Synthesis for a Class of Cascade Switched Nonlinear Systems with Actuator Saturation. Circuits Syst Signal Process 33, 2961–2970 (2014). https://doi.org/10.1007/s00034-014-9776-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9776-7

Keywords

Search

Navigation