Skip to main content

Decentralized Robustification of Interconnected Time-Delay Systems Based on Integral Input-to-State Stability

  • Chapter
Delay Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 1))

Abstract

This article deals with interconnected systems described by retarded nonlinear equations with discontinuous right-hand side. The problem of feedback control redesign to achieve ISS (input-to-state stability) and iISS (integral input-to-state stability) with respect to additive disturbances acting on each subsystem is solved. It is shown that it is possible to design a decentralized controller accomplishing the robustification whenever a small-gain condition is satisfied.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Heemels, W.P.M.H., Weiland, S.: Input-to-state stability and interconnections of discontinuous dynamical systems. Automatica 44, 3079–3086 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ito, H., Jiang, Z.P.: Necessary and sufficient small gain conditions for integral input-to-state stable systems: a Lyapunov perspective. IEEE Trans. Autom. Control. 54, 2389–2404 (2009)

    Article  MathSciNet  Google Scholar 

  3. Ito, H., Jiang, Z.P., Dashkovskiy, S., Rüffer, B.: Robust stability of networks of iISS systems: construction of sum-type Lyapunov functions. IEEE Trans. Autom. Control 58 (2013), doi:10.1109/TAC.2012.2231552

    Google Scholar 

  4. Ito, H., Jiang, Z.P., Pepe, P.: A small-gain methodology for networks of iISS retarded systems based on Lyapunov-Krasovskii functionals. In: Proc. 18th IFAC World Congress, pp. 5100–5105 (2011)

    Google Scholar 

  5. Ito, H., Pepe, P., Jiang, Z.P.: A small-gain condition for iISS of interconnected retarded systems based on Lyapunov-Krasovskii functionals. Automatica 46, 1646–1656 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ito, H., Pepe, P., Jiang, Z.P.: Decentralized iISS robustification of interconnected time-delay systems: a small-gain approach. In: Proc. 10th IFAC Workshop on Time Delay Systems, pp. 219–224 (2012)

    Google Scholar 

  7. Karafyllis, I., Jiang, Z.P.: A new small-gain theorem with an application to the stabilization of the chemostat. Int. J. Robust and Nonlinear Contr. 22, 1602–1630 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kim, A.V.: Functional differential equations, application of i-smooth calculus. Kluwer, Dordrecht (1999)

    Book  MATH  Google Scholar 

  9. Kolmanovskii, V., Myshkis, A.: Introduction to the theory and applications of functional differential equations. Kluwer, Dordrecht (1999)

    Book  MATH  Google Scholar 

  10. Pepe, P.: Input-to-state stabilization of stabilizable, time-delay, control affine, nonlinear systems. IEEE Trans. Automat. Contr. 54, 1688–1693 (2009)

    Article  MathSciNet  Google Scholar 

  11. Pepe, P.: On the actuator disturbance attenuation for systems described by neutral equations. IMA J. Mathematical Control and Information 28, 163–181 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pepe, P., Ito, H.: On saturation, discontinuities and delays in iISS and ISS feedback control redesign. IEEE Trans. Automat. Contr. 57, 1125–1140 (2012)

    Article  MathSciNet  Google Scholar 

  13. Pepe, P., Jiang, Z.P.: A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems. Systems & Contr. Letters 55, 1006–1014 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sontag, E.D.: Smooth stabilization implies coprime factorization. IEEE Trans. Automat. Contr. 34, 435–443 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sontag, E.D.: Comments on integral variants of ISS. Systems & Contr. Letters 34, 93–100 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Surkov, A.V.: On the stability of functional-differential inclusions using invariantly differentiable Lyapunov functionals. Differential Equations 43, 1079–1087 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hiroshi Ito .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ito, H., Pepe, P., Jiang, ZP. (2014). Decentralized Robustification of Interconnected Time-Delay Systems Based on Integral Input-to-State Stability. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-01695-5_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01694-8

  • Online ISBN: 978-3-319-01695-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics