Skip to main content
SpringerLink
Log in

Exponential Formula for Impulsive Differential Inclusions

  • Conference paper
Large-Scale Scientific Computing (LSSC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5910))

Included in the following conference series:

  • 2104 Accesses

Abstract

This paper studies the graph of the reachable set of a differential inclusion with non-fixed time impulses. Using approximation in L 1–metric, we derive exponential characterization of the reachable set.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aubin, J.-P.: Impulsive Differential Inclusions and Hybrid Systems: A Viability Approach. Lecture Notes, Univ. Paris (2002)

    Google Scholar 

  2. Baier, R., Donchev, T.: Discrete Approximation of Impulsive Systems (submitted)

    Google Scholar 

  3. Clarke, F.: Optimization and nonsmooth analysis. John Wiley & Sons, Inc., New York (1983)

    MATH  Google Scholar 

  4. Deimling, K.: Multivalued Differential Equations. De Gruyter, Berlin (1992)

    MATH  Google Scholar 

  5. Donchev, T.: Approximation of the Solution Set of Impulsive Systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2007. LNCS, vol. 4818, pp. 309–316. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Donchev, T.: Impulsive differential inclusions with constrains. EJDE 66, 1–12 (2006)

    Google Scholar 

  7. Donchev, T., Farkhi, E., Wolenski, P.: Characterizations of Reachable Sets for a Class of Differential Inclusions. Functional Differential Equations 10, 473–483 (2003)

    MATH  MathSciNet  Google Scholar 

  8. Lakshmikantham, V., Bainov, D., Simeonov, P.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)

    MATH  Google Scholar 

  9. Lempio, F., Veliov, V.: Discrete approximations of differential inclusions. Bayreuther Mathematische Schiften, Heft 54, 149–232 (1998)

    MATH  MathSciNet  Google Scholar 

  10. Pereira, F., Silva, G.: Necessary Conditions of Optimality for Vector-Valued Impulsive Control Problems. System Control Letters 40, 205–215 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Plotnikov, V., Kitanov, N.: On Continuous dependence of solutions of impulsive differential inclusions and impulse control problems. Cybernetics System Analysis 38, 749–758 (2002)

    Article  MathSciNet  Google Scholar 

  12. Plotnikov, V., Plotnikov, A., Vitiuk, A.: Differential Equations with Multivalued Right-Hand Side. Asymptotical Methods. Astro Print, Odessa (1999) (in Russian)

    Google Scholar 

  13. Wolenski, P.: The exponential formula for the reachable set of a Lipschitz differential inclusion. SIAM J. Control Optim. 28, 1148–1161 (1990)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Architecture and Civil Engineering, 1 “Hr. Smirnenski” str., 1046, Sofia, Bulgaria

    Tzanko Donchev

Authors
  1. Tzanko Donchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads - Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Donchev, T. (2010). Exponential Formula for Impulsive Differential Inclusions. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12535-5_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12534-8

  • Online ISBN: 978-3-642-12535-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation