Skip to main content
SpringerLink
Log in

Sampled-Data Control of Switched Affine Systems

  • Chapter
  • First Online:
Book cover Hybrid Dynamical Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 457))

  • 1573 Accesses

Abstract

This chapter considers the stabilization problem for switched affine systems with a sampled-data switching law. The switching law is assumed to be a function of the system state at sampling instants. Sampling interval may be subject to variations or uncertainty. Switching law design criteria, taking into account the sampled-data implementation and uncertainties, are provided. Numerical examples illustrate the approach.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Åström, K.J., Wittenmark, B.: Computer-Controlled Systems. Prentice Hall, New Jersy (1997)

    Google Scholar 

  2. Deaecto, G.S., Geromel, J.C., Garcia, F.S., Pomilio, J.A.: Switched affine systems control design with application to dc-dc converters. Control Theory Appl. IET 4(7), 1201–1210 (2010). July

    Google Scholar 

  3. Defoort, M., Djemai, M., Floquet, T., Perruquetti, W.: On finite time observer design for multicellular converter. In: 11th IVSS, pp. 56–61 (2010)

    Google Scholar 

  4. Fridman, E.: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Syst. Control. Lett. 43, 309–319 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46(2), 421–427 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fridman, E., Seuret, A., Richard, J.-P.: Robust sampled-data stabilization of linear systems. Automatica 40, 1441–1446 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fujioka, H., Kao, C.-Y., Almer, S., Jonsson, U.: Robust tracking with performance for pwm systems. Automatica 45(8), 1808–1818 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hauroigne, P., Riedinger, P., Iung, C.: Switched affine systems using sampled-data controllers: robust and guaranteed stabilization. IEEE Trans. Autom. Control. 56(12), 2929–2935 (2011)

    Google Scholar 

  9. Hetel, L., Daafouz, J., Iung, C.: Stabilization of arbitrary switched linear systems with unknown time varying delays. IEEE Trans Autom Control 51(10), 1668–1674 (2006)

    Article  MathSciNet  Google Scholar 

  10. Hetel, L., Fridman, E.: Sampled-data control of switched affine systems: a continuous-time approach. In: Proceedings of the 7th IFAC Symposium on Robust Control Design, Aalborg, Denmark (2012)

    Google Scholar 

  11. Hetel, L., Kruszewski, A., Perruquetti, W., Richard, J.: Discrete and intersample analysis of systems with aperiodic sampling. IEEE Trans. Autom. Control. 56(7), 1696–1701 (2011)

    Google Scholar 

  12. Mirkin, L.: Some remarks on the use of time-varying delay to model sample-and-hold circuits. IEEE Trans. Autom. Control. 52(6), 1109–1112 (2007)

    Google Scholar 

  13. Naghshtabrizi, P., Teel, A., Hespanha, J.P.: Exponential stability of impulsive systems with application to uncertain sampled-data systems. Syst. Control. Lett. 57(5), 378–385 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Oishi, Y., Fujioka, H.: Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities. Automatica 46(8), 1327–1333 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Patino, D., Riedinger, P., Iung, C.: Predictive control approach for multicellular converters. In: 34th Annual Conference of IEEE, Industrial Electronics, IECON 2008, pp. 3309–3314, november 2008

    Google Scholar 

  16. Patino, D., Riedinger, P., Iung, C.: Practical optimal state feedback control law for continuous-time switched affine systems with cyclic steady state. Int. J. Control. 82(7), 1357–1376 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Pettersson, S., Lennartson, B.: Stability and robustness for hybrid systems. In: Proceedings of the 35th Conference on Decision and Control, pp. 1202–1207, December 1996

    Google Scholar 

  18. Seuret, A.: A novel stability analysis of linear systems under asynchronous samplings. Automatica 48(1), 177–182 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C.: Stability criteria for switched and hybrid systems. Invited paper for SIAM Review 49(4), 545–592 (2007)

    Google Scholar 

  20. Sira-Ramirez, H., Rios-Bolivar, M.: Sliding mode control of dc-to-dc power converters via extended linearization. IEEE Trans. Circuits Syst. I: Fundam. Theor. Appl. 41(10), 652–661 (1994)

    Google Scholar 

  21. Sivashankar, N., Khargonekar, P.P.: Robust stability and performance analysis of sampled-data systems. IEEE Trans. Autom. Control. 38(1), 58–69 (1993)

    Google Scholar 

Download references

Acknowledgments

The research leading to these results has received funding from the European Community’s \(7\)th Framework Programme (grant agreement No 257462) HYCON2 Network of Excellence and Israel Science Foundation (grant No 754/10).

Author information

Authors and Affiliations

  1. Laboratoire d’Automatique Génie Informatique et Signal (CNRS LAGIS UMR 8219), Ecole Centrale de Lille, Avenue Paul Langevin, BP 48, 59651, Villeneuve d’Ascq Cedex, France

    Laurentiu Hetel

  2. Department of Electrical Engineering and Systems, Tel Aviv University, 69978, Ramat Aviv, Tel Aviv, Israel

    Emilia Fridman

Authors
  1. Laurentiu Hetel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emilia Fridman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laurentiu Hetel .

Editor information

Editors and Affiliations

  1. LAMIH CNRS UMR 8201, University of Valenciennes and Hainaut-Cambresis, Valenciennes, France

    Mohamed Djemai

  2. LAMIH UMR-CNRS 8201, University of Valenciennes and Hainaut-Cambresis, Valenciennes, France

    Michael Defoort

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Hetel, L., Fridman, E. (2015). Sampled-Data Control of Switched Affine Systems. In: Djemai, M., Defoort, M. (eds) Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 457. Springer, Cham. https://doi.org/10.1007/978-3-319-10795-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10795-0_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10794-3

  • Online ISBN: 978-3-319-10795-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation